{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 15\n",
    "\n",
    "# SVD分解\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41270862-d3e7-48a3-89f3-9a009139df69",
   "metadata": {},
   "source": [
    "该代码实现了对一个给定矩阵 $A$ 的奇异值分解（SVD），并逐步展示了 SVD 各部分对二维空间的几何变换过程。代码首先生成一个 $1 \\times 1$ 的单位网格，足够大的坐标轴范围，并在单位圆上生成一组散点，表示初始点集。SVD 分解将矩阵 $A$ 表示为三个部分的乘积：\n",
    "\n",
    "$$\n",
    "A = U \\Sigma V^T\n",
    "$$\n",
    "\n",
    "其中：\n",
    "- $U$ 是一个正交矩阵，表示输出空间的旋转。\n",
    "- $\\Sigma$ 是包含奇异值的对角矩阵，表示在每个方向上的缩放因子。\n",
    "- $V^T$ 是另一个正交矩阵，表示输入空间的旋转。\n",
    "\n",
    "代码分为几个步骤展示 SVD 的几何变换效果：\n",
    "\n",
    "1. **生成并展示初始网格和单位圆**：在 $[-8,8] \\times [-8,8]$ 的坐标系中生成一个 $1 \\times 1$ 的单位网格，并以 HSV 渲染生成单位圆上的散点，表示初始的坐标和点集。\n",
    "\n",
    "2. **直接应用矩阵 $A$**：代码直接对初始网格、单位圆散点和坐标轴向量应用 $A$，展示出矩阵 $A$ 的整体作用效果，包括旋转、缩放和偏移。\n",
    "\n",
    "3. **逐步展示 SVD 的几何变换**：\n",
    "   - **应用 $V^T$**：代码首先对网格和散点应用 $V^T$，即一个旋转矩阵，展示单位圆和网格的旋转效果：\n",
    "     $$\n",
    "     X' = V^T X\n",
    "     $$\n",
    "   - **应用 $\\Sigma$**：接着，代码将 $\\Sigma$ 的缩放效果应用于旋转后的网格和散点，将其沿奇异值方向拉伸或压缩：\n",
    "     $$\n",
    "     X'' = \\Sigma X'\n",
    "     $$\n",
    "   - **应用 $U$**：最后，代码应用 $U$，将缩放后的结果旋转到最终位置，得到完整的变换效果：\n",
    "     $$\n",
    "     X''' = U X''\n",
    "     $$\n",
    "\n",
    "4. **展示最终的变换结果**：代码在每一步中显示变换后的网格、散点和坐标轴向量，完整展示了 $A$ 的分解对几何空间的作用。这些可视化展示了矩阵 $A$ 如何通过旋转、缩放和再次旋转的过程，将初始的单位网格和单位圆变换为其最终形态。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "12cfc5cc-a245-455e-8e19-9eb01d683f79",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f92ce86e-1300-4a63-aaf7-b361d3fab533",
   "metadata": {},
   "source": [
    "## 定义可视化函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fd5e25e3-0dd1-4eb0-9bc1-66e28526c899",
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize(X_grid, X_circle, X_vec, title_txt):\n",
    "    fig, ax = plt.subplots()  # 创建绘图窗口\n",
    "    \n",
    "    # 绘制变换后的网格\n",
    "    for i in range(X_grid.shape[0]):\n",
    "        plt.plot(X_grid[i, :, 0], X_grid[i, :, 1], 'k-', linewidth=0.5)  # 绘制网格行\n",
    "    for j in range(X_grid.shape[1]):\n",
    "        plt.plot(X_grid[:, j, 0], X_grid[:, j, 1], 'k-', linewidth=0.5)  # 绘制网格列\n",
    "    \n",
    "    # 绘制变换后的散点，并用HSV色彩渲染\n",
    "    colors = plt.cm.hsv(np.linspace(0, 1, X_circle.shape[0]))  # HSV 色彩映射\n",
    "    for i in range(X_circle.shape[0]):\n",
    "        plt.plot(X_circle[i, 0], X_circle[i, 1], 'o', color=colors[i], markersize=5)  # 绘制散点\n",
    "    \n",
    "    # 绘制变换后的坐标轴方向向量\n",
    "    plt.quiver(0, 0, X_vec[0, 0], X_vec[0, 1], angles='xy', scale_units='xy', scale=1, color=[0, 0.4392, 0.7529])  # 绘制第一个向量\n",
    "    plt.quiver(0, 0, X_vec[1, 0], X_vec[1, 1], angles='xy', scale_units='xy', scale=1, color=[1, 0, 0])  # 绘制第二个向量\n",
    "    \n",
    "    # 绘制 x 和 y 轴\n",
    "    plt.axvline(x=0, color='k', zorder=0)  # 绘制 x 轴\n",
    "    plt.axhline(y=0, color='k', zorder=0)  # 绘制 y 轴\n",
    "    \n",
    "    # 设置标签和网格\n",
    "    plt.ylabel('$x_2$')  # y轴标签\n",
    "    plt.xlabel('$x_1$')  # x轴标签\n",
    "    ax.set_aspect(1)  # 设置坐标轴比例\n",
    "    ax.set_xlim([-3, 3])  # x轴范围\n",
    "    ax.set_ylim([-3, 3])  # y轴范围\n",
    "    ax.grid(linestyle='--', linewidth=0.15, color=[0.8, 0.8, 0.8])  # 添加网格\n",
    "    plt.title(title_txt)  # 设置图标题\n",
    "    # plt.savefig(title_txt + '.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd62991c-584d-4b32-a47a-3e87a855f822",
   "metadata": {},
   "source": [
    "## 创建一个包含足够大的1x1网格区域"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "074ab85d-b20d-4732-ae13-e85b81587fa3",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_vals = np.arange(-8,8+1)  # x轴网格点\n",
    "y_vals = np.arange(-8,8+1)  # y轴网格点\n",
    "X1, X2 = np.meshgrid(x_vals, y_vals)  # 生成网格\n",
    "X_grid = np.stack([X1, X2], axis=2)  # 将网格堆叠为3维数组"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7e82949-2a67-49a6-a7da-d26ec43216bd",
   "metadata": {},
   "source": [
    "## 创建初始的散点（单位圆上的点）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1636057e-64d5-457c-9634-134614dc41b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.linspace(0, 2 * np.pi, 30)  # 生成角度\n",
    "circle_x1 = np.cos(theta)  # 计算圆上的 x 坐标\n",
    "circle_x2 = np.sin(theta)  # 计算圆上的 y 坐标\n",
    "X_circle = np.array([circle_x1, circle_x2]).T  # 创建单位圆散点坐标"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6567a970-3c6d-4ae3-ad20-47869b61e227",
   "metadata": {},
   "source": [
    "## 定义初始坐标轴向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ad3f5c1e-d00a-4f56-bcda-a24a697dd46d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_vec = np.array([[1, 0],\n",
    "                  [0, 1]])  # 初始坐标轴向量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1acd431b-8829-4a60-8cb3-2d39caf959c9",
   "metadata": {},
   "source": [
    "## 绘制原始网格、散点和坐标轴向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "56c8397c-c927-48ba-8d33-3d13596bbb6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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CZk8XFxERM0TtpBW3283zzz9PRUWF32u7Kisr633PmcfjobS0lG7duoW8ZJOIiLQftm1z6NAh+vTp0/TFJsL/BQ0ts3nzZrtz5862w+GwU1JS7Ndee81v25qvl9GPfvSjH/3E1s/OnTubXD+ibkizqqqKHTt2cODAAV588UWWLFnC+vXrGTJkSKO2DXt4ZWVlpKens3PnzlZb3igaVFdXM3XqVJ577rlIhxI2JuZcUVHB4MGDqaioYOfOnXTu3DnSIYWNicfbxJwBSktL6d+/PwcOHGjyykRRN6TZsWPH2kkrI0aMoLCwkIceeojFixc3apuQkOBz/cOaWZ6mqK6uJj4+XjnHOIfDgWVZWJZFcnKycQXPtONtYs5A7eLjzTktFVWXJfhi23a9XpyIyaJswEYkrKKqh3f33XczYcIE+vXrx6FDh1i+fDnr1q1j1apVkQ5NpF3QZCwR/6Kq4H399ddcccUV7Nmzh5SUFIYOHcqqVas488wzIx2aiIi0c1FV8Gq+WViaxrZt44a6TMwZzO3hmXi8TcwZWjZsH/Xn8EREREKhgmeAmpl7JjExZzB30oqJx9vEnKFloxgqeCIiYgQVPJEYYmoPTyQUKngiMcTEIS6RUKngiYiIEVTwRGKIhjRF/FPBE4khGtIU8U8FT0REjKCCZwATV2QwMWcwt4dn4vE2MWfQSisiIiJBqeCJiIgRVPAMYOISRCbmDObO0jTxeJuYM2hpMRE5zNSCJxIKFTyRGGLiJ36RUKngiYiIEVTwRGKIhjRF/FPBE4khGtIU8U8FT0REjKCCJyIiRlDBM4CJSxCZmDOYO6Rp4vE2MWfQ0mIiIiJBqeCJiIgRVPAMYOISRCbmDODxeCIdQkSYeLxNzBm0tJiIHGbiG6BIqFTwRETECCp4IjHExFl7IqFSwROJIRrSFPFPBU9ERIyggicSQzSkKeKfCp4BTFyRwcScAeLizPyTNvF4m5gzaKUVERGRoFTwRETECCp4BjBxRQYTcwZzz+GZeLxNzBm00oqIiEhQKngiImIEFTyRGGLqkKZIKFTwRGKIied0REKlgiciIkZQwROJIRrSFPFPBU8khmhIU8Q/FTwDmLgEkYk5g7kFz8TjbWLOoKXFREREglLBExERI6jgGcDEJYhMzBnMnbRi4vE2MWfQ0mIiIiJBqeCJxBBTe3gioVDBE4khJg5xiYRKBU9ERIyggicSQzSkKeJfVBW8efPmMXLkSLp27UqPHj248MIL2bp1a6TDEmk3NKQp4l9UFbz169dz4403smHDBtasWUN1dTXjxo2joqIi0qGJiEg71yHSATTFqlWr6v1eUFBAjx49+Pjjjzn11FMjFFX7Z+ISRCbmDOb28Ew83ibmDC0bto+qgtdQWVkZAKmpqT7vr6yspLKysvb3gwcPAuByuXC5XEHfHOr+wwZqG2q75rZt6T6rq6uxbbv2NpTnb+85BWtbN+fW2mewtm2dU7B21dXVJCcnU1lZidvtrpd7c58/0jmFuk9fx9tf22jJKVjbmpxb872sKW0j9fcU6BgHY9lR+hHBtm0uuOACvvvuO9555x2fbebMmcPcuXMbbR83bhzx8fFRf+BD3adt2xQWFvKrX/0qZnIK1rZuzq21z2BtI/2m43a7WbduHVVVVYwfPx6Hw9Hi5490Tk3ZZ8Pj7a9tNOUUbJ+FhYWMHDkyZnKq29Zfu6qqKlavXk1ZWRnJyckB99VQ1Ba8G2+8kddee413332Xvn37+mzjq4fXr1+/Zv1DRbPq6momTpzIK6+8EulQwsbEnCsqKjjqqKOoqKjgwIEDdO7cOdIhhY2Jx9vEnAFKS0vp1q1bs97Ho3JI86abbuLll1/m7bff9lvsABISEkhISAhjZCKRFaWfX0XCIqoKnm3b3HTTTaxYsYJ169bRv3//SIck0q6YOmlFJBRRVfBuvPFGli1bxksvvUTXrl3Zu3cvACkpKSQmJkY4OhERac+i6jq8xx57jLKyMrKzs+ndu3ftz7PPPhvp0ETaBQ1pivgXVT08/TGLBKYhTRH/oqqHJyIi0lwqeAYwcUUGE3MGc3t4Jh5vE3OGlo30qeCJiIgRVPBERMQIKngGsCzLuKEuE3MGcyd2mXi8TcwZWjZsr4InEkNMLXgioVDBE4khJn7iFwmVCp6IiBhBBU8khmhIU8Q/FTyRGKIhTRH/VPBERMQIKngiImIEFTwDmLgEkYk5g7lDmiYebxNzBi0tJiIiEpQKnoiIGEEFzwAmLkFkYs4AHo8n0iFEhInH28ScQUuLichhJr4BioRKBU9ERIyggicSQ0yctScSKhU8kRiiIU0R/1TwRETECCp4IjFEQ5oi/qngGcDEFRlMzBkgLs7MP2kTj7eJOYNWWhEREQlKBU9ERIyggmcAE1dkMDFnMPccnonH28ScQSutiIiIBKWCJyIiRlDBE4khpg5pioRCBU8khph4TkckVCp4IiJiBBU8kRiiIU0R/1TwRGKIhjRF/FPBM4CJSxCZmDOYW/BMPN4m5gxaWkxERCQoFTwRETGCCp4BTFyCyMScwdxJKyYebxNzBi0tJiIiEpQKnkgMMbWHJxIKFTyRGGLiEJdIqFTwRETECCp4IjFEQ5oi/qngicQQDWmK+KeCJyIiRlDBM4CJSxCZmDOY28Mz8XibmDNoaTEREZGgVPAMYOKKDCbmDOZOWjHxeJuYM2ilFRERkaBU8ERiiKk9PJFQqOCJxBATh7hEQqWCJyIiRoiqgvf2229z3nnn0adPHyzLYuXKlZEOSaRdqRnSPGhtYwMzWcMUNjCTAxRFODKRyOsQ6QCaoqKigl/84hdcddVVXHzxxZEORyQsvqaId8hnH8WkkcEp5NKTgT7bWpbFidM8rEwchoUF2IDFJuaTjZPB5IQzdJF2JaoK3oQJE5gwYUKkwxAJm3coYCnTsbCwsbGw+AfzuQonWT6KV7dj3ExZ7AHLW+rqWkcevckihUyfz/UjRewjnyqK6UgGaeTSyU9hFYlGUVXwmqqyspLKysra3w8ePAiAy+XC5XIFPcFfd8ZboLahtmtu25bu0+Vy4fF4qK6ujpmcgrWtm3Nr7TNY29be59cUsbTDdGzLU1u87MP/KSCPY9wn0d0eUPuY6upqRufF4Xeipm3xmecJRnr+0Oj591tL2Rl3LdTpFe5lPv08T9DNntZqOYXStjn7rK6ubnS8/bVt69deuPZZ8xpvzfeyprSN1N+Ty+UK+PhAYrrgzZs3j7lz5zbaPnXqVOLj46P+wIe6T4/Hw8aNG5k4cWLM5BSsbd2cW2ufwdqG0s7Vp4LyM3dS3eMHOnyTSNc1/Yjf08Vn287TviDpIhvL0eBOCzxum1tXnEv5k4NrN7vdbvpfVYG/MNweN6+/+zT/s2BLvVhTe5dz4+PriGvwONuGr6zp3H7903y3p3PA3EPNP5S2zdmnbduNjre/trFSHOq+xmMlp7pt/bWr24lpKsuO0gt3LMtixYoVXHjhhX7b+Orh9evXj7KyMpKTk8MQZfvgcrmYOHEir776aqRDCZv2mPMKCpjdYHjSxuY+nFzoY3jycaZQyHPYeBrdZxHHSC7lOp6p3VZRUcHiJ7qRcFMlcT4+ylo4OIHbOYl59bbvYiZ7WQC4fUTtoBe307fBY9qb9ni825qJOQPs37+ftLS0Zr2PR9UszaZKSEggOTm53o+JTFyCqL3l/BVFzGY6Hjy4cde7nUUeO9jW6DFpZByeeNKYhUUaGY22n/hUvLeH5/NjrM1x5DXaWkWxvwcA9uH727f2drzDwcScQUuLibR7fyc/YPF6EWej7aeQi+2nENnYnNKgeFklJZz4ZRybr4kD4rBwYNW5zcbpc8JKRzLAT2xgHb7fN49dRLVnJi7PFKo9M/HYuvxB2q+oOodXXl7Otm0/fRLevn07mzZtIjU1lfT09AhGJhJYCcUBi1eJj15UTwZyFU4KyGs0DHoVTno2KF6OVavAstj91zjum/B7/nNJGYcopisZHEee39mZaeSyl/l+IrdJ89ErBHDbBVTb06k70cVtz6cDThxWjp/9iUROVBW8jRs3MmbMmNrfb731VgCmTZvG0qVLIxSVSHB9ggxP9vHTi8oih4Fk8Q7OOtfh5TUqdgCOf/yj9v9Tn/2YHpc8H1JsnRhIBk6KyaNu8QKbDJx08vFcHrvocLFrfH6x2s4jjiwsy3eBFYmUqCp42dnZWhxXotJF5FLgpxdlY3Oxn14UQE8yuSTYpJHvv8exdi3ujh0BcPzzn+ByQXx8SPGlkUMXstiHs851eHk+ix2Ax84n0DCo23bSwWrfE13EPFFV8ETamyK2UcBTFLODDNK5iisY6KNIHM1A7sPJLB/Dk/fhJN1PYQnZm29i/fgjJCQAYB04AO+9B9nZIe+iE5khz8a0g0x0saNgoouYRwVPpJkKeIprmFGvgC1gIX/hUXL4daP2F5LDMLJ4ESclFNOHDC4mr+XFDsDX1PRXXmlSwWsKK8hEFyvARBeRSFHBE2mGIrZxDTPw+DiHdTU3ksUoMhnQ6L50Mrmlta9ps23/Be/BB1v3uQ6Ls3Jx2/4nujgs/0O0IpGiyxIMYNu2cec+2zrnAp4KOAkln7+22XM38sknUFICgG1ZPw00FhXB1q1t8pRx1kA6WE68byGOercdLGfYJ6zoNW6OluSsHp5IMxSzI+BlBsXsCF8wr7wS+L5Bg9rkaR1WDnFk4bad2BRjkYHDyvNf7CqLYH8+VBVDxwzolgsJWpxawkcFT6QZMkgP2MPLIIzXhb7yCvTsiXvIEPj0UwCqzziDDps2eYc6/+u/2uypLSsztNmY+wtgZ/1r9vhmPvRzQrecNotPpC4NaRrAxCWI2jrnq7giYA8vlyvb7LnrKS+HK6+E//yH6vPPx/J4sAD3ZZfB9u1w/vnQgsV2W0Vl0eFi58G7Xmed2515UNl4WbWm0mvcHFpaTCTMBpLJX3iUOOJw4Kh3+xce9TlhpU106QK//S0kJXl/r/tm0KUL3Hpr7aUKEbM/8DV77G+8rJpIW9CQpogPRewin9cpZi8Z9CKXsxlI33ptcvg1WYwin7/WXoeXy5XhK3bRoqqYQNfsee8XaXsqeCINFPAPprOg3iJb81mOk9vJYUK9tpkM4H9o/J2LEdMeZ+11zCBgD69jRvhiEaNpSFOkjiJ2MZ0Fh7++x1PvNo8FbGNXpEMMrD2e0+mWS8AeXjddsyfhoYInUkc+rwfqi+Dk9XCGExsSBnpnY/q4Zo9+TkjQItMSHhrSFKmjmL2B+iIUszec4TRdexzSBO+lB12yvBNUaq/Dy1Oxk7BSwTOAiSsyNDfnDHoF7OFl0KtFcbU1Oy7Ob8GOuIRM6BPkmr2yItiaD+XF0CUDBuVCSvCL0/UaN4dWWhFpJbmczXyW+7zPBvI4O7wBmWRrAbzT4OL0zfPhVCccmxPZ2CQm6ByeSB0D6YuT2xtcXxdHHHE4uZ3MBpcmSCspK/IWO9sDtrv+7dt5UNbyi9NF1MMzgIkrMrQk5xwmkMXPcda5Di+Ps6Oi2Fm27XdItl3bGuTi9K1O+JX/4VC9xs3RkpxV8ER88H4V6jWRDsMc5cUEvHShvDh8sUjM0pCmiERelwwC9vC6ZIQvFolZ6uGJkYr4hnw+pJhSMkgllxMZSI9Ih9Vy0Tprb1Cud4KKTzYM0sXp0nIqeGKcAjYwneVYWNjYWFjM502cTCGHEyMdXstE6zmdlIHe2Zhv51Fvlia2d3uKrteTllPBE6MU8Q3TWY4Hm5/OGXlv83iGLI4hk+4Ri89ox+ZAzyzvBJXa6/DyVOyk1ajgiVHy+fDwF7c2HvqzsHCygXmcF/7AWku0DmnWSMkMOBtTpCU0aUWMUkxpwC9uLaY0zBG1smgd0hQJAxU8A5i4BJG/nDNIPdzDa8zCIoPUtg6tTdmW1X6XFmtDeo2boyU5q+CJUXI5MWAPL4+TwhyRhOzrIvj7THhiivf266JIRyRRRufwxCgD6YGTKeTxTL1ZmjY2TqZowkp79V4BPDndO2Rr297bVfNhmhNG50Q6OokSKngGMHEJokA553AiWRyDkw211+HlcVJMFLuoXVoskK+LvMXO9jScWAtP5sHALKzUDL3GDaGlxUSaKJPu0T0b0yTv5R/u2fm4z7LgXSec//uwhyXRR+fwRGJJLE5i2FfsPy/b9t4vEgIVPJFYEotDXGkZ/vOyLO/9IiFQwZOYV8RBZvIpU3iHmXxKEQcjHZI0xejcwD28LK2zKaFRwZOYVsCXDOZlFrCF5/iKBWxhMC+zlC8jHVrbiMUhzZ4DvbMxrTiIc9S/neaEHlp6TEKjSSsSs8p7d2E6H+ABGq+b+QFZ9CCTrhGKro3E4pAmeC89GJjlnaCyr9g7jJmVp2InTaKCJzFr55n9g6ybuY15/DL8gUnz9MiEi7TOpjSfhjQNYOISRLZt80OPzgFWVYFiysMbVBhoaTFzmJgzaGkxEZ8Sv6kIsG4mZNAlvAGJSERpSNMAJq7IYFkW/dZsZ/ukIT7v966bGXvnf2JypRV/viqCl/KhpBhHr3T6VFdEOqKwMvHvGrTSiohPXfaU42QUeXxweL3Mmu/QtnEyKvYmrJhkZQHc99PampZl8bjbDS8thQtyIh2dtFMqeBLTchhAFj1wso1iysmgC3lkxm6xM+GczldF3mLn8dRuqv3MPzcPfpkF6bHXe5eWU8GTmJdJV3NmY5owxPVSvs88LfBuX+mE32g2pzSmSSsiEl1KigOvvFJSHM5oJIqo4InEEhOGNPtkBF5bs09GOKORKKKCJxJLTBjSvMD32po2eLdfqLU1xTcVPIlJRVTx+ZUTmEIJM/mWIqoiHZK0lqMHwmwnxMWBwwFxcdgOh7fgzXZqwor4pUkrBjBtRYYCypju2It9UTbbOYQFzKcUJ73IISXS4bUpY1ZauSDHOxtzpRNKivH07Md1bxTyF4MuSTDt77pGS3JWwZOYUkQV09mLxwJqPvUflsdeskgkk46RCk9aU3pm7WxMj8vFnjcnRjggae80pCkxJZ8yvyuNWICTsnCGIyLtiAqeAUxagqgYl98hPfvw/bHMqKXF6jDpNV7DxJyhZUuLNavg/fDDD+zevbvR9s8++6zZgYi0hgziA/bwMogPZzjhZ+A5HZFQNbngvfDCCxx77LGcffbZDB06lA8//LD2viuuuKJVgxNpqlxSDk9Pb3yfDeTF+KSVaL8sobTCxePvlbDrQGWkQ5EY1OSC99///d988skn/Otf/yI/P5/c3FyWLVsGtGz2TKgWLVpE//796dSpE8OHD+edd95p8+eU6DGQjjjpRRxgud3EAQ68L3QnvTRhpZ1L7RzPS//eR7+5Gxj2wMfM/kcxG3ccwuMJ8N6y5i0cWRNwvrkRRo2DNW+FL2CJKk2epelyuejevTsAI0aM4O233+aiiy5i27ZtbT6e/Oyzz3LzzTezaNEiRo8ezeLFi5kwYQJbtmwhPT29TZ9bokcOKZzk7si5KwoYOelCMognjxQzil0MDGnOHp/Bqi++49Pd5Xy6u5z7Vn9F7+SOnDMklfN+1o0zjj2SpI4Ob+PcGVDwAgDdATZshnFTIW8SLHk4YjlI+9TkgtejRw82b97M0KFDAejWrRtr1qxh2rRpbN68udUDrOuPf/wjeXl5TJ8+HYCFCxfyxhtv8NhjjzFvXuiLxVZUVOBwONoqzHbH7XbjdrupqDDn+8L6uN0cW/AqS86edniLi4oYn7Diqaoi8fCHzrte38FLJRsiHFHzHf7Wn1p7DlaxZMNelmzYS6cOFtkDkrn60BYmFryA1eBrfm1scD7PjxeejWfMqWGPPVxM/LsG+P7775v9WMsOcRzy0KFDdO3alV27dtGhQwd69erVqM17773H6NGjmx1MIFVVVSQlJfH8888zceJP19v89re/ZdOmTaxfv77RYyorK6ms/OlcwMGDB+nXrx8pKSlYllV74WZNz7Tu/0P92UAej8dnO9u2iYv7aWS47j+nr33X3WdNW38x1N0WSrua7Q3bpaSk8O2335KQkBAzOQU7TsnJybU5x0pOvvZdN6df2jbnJafgrIzjiHNn8e+0Y7zt8E7YqTsAU5N+zX31/t+qvw3bTzsf+/TXru4+ATy273Y2EFd3n7X/adxuzVN3MnJPsc9vtbexKXT8yJmd299xaq3XXnJyMvv27SMhISFmcqr7/P7ade3ald27d1NWVkZycjJNEXIP75RTTmHVqlX07dvXb5u2KnYA+/btw+1207Nnz3rbe/bsyd69e30+Zt68ecydO7fR9vLycqOm81ZVVVFVVUV1dXWkQwmbyspK43J+B/igqooqK4G4tx5r3KB+N8i/hn8aobZtzX066symbdTWhh8P0fPrEggw67an2+L772O391PzGne5YnvkoqG6nZimCrngjRgxghNPPJE33niDwYMH127/9NNPueeee3j99debHURTNCxUDT+d1DVz5kxuvfXW2t9reng7d+5s8ieDaFZdXc3kyZN54YUXIh1K2JiYc0VFBYMGDaK6vJzdH75K586dIx1Ss2wqqSBr0ef1th2Z6ODMgSlMGHwEZwxM5sjEDnQaez585P9SqL6/GsaBt15u63AjxsTXOEBpaWmz52yEXPCWLFnC3LlzycrKYuXKlfTo0YN7772XF198kfPPP79ZT94UaWlpOByORr25b775plGvr0ZCQkLtkFZdnTt3jto3g+ZwuVw4HA6jct5S6aJoai7Trc5kxEFuPAw057RtVL/G57+9HYBBPRI572fdOHdIN0b3T6GDo8EH2/++xztBpf7gKeC9+N7xP7+L2n+DUJj4dw3w448/NvuxTZq0Mnv2bDp27MiZZ56J2+1m/PjxFBYWMmzYsGYHEKqOHTsyfPhw1qxZU+8c3po1a7jgggva/PklehRUwfQfO2CfcxHbXd63wvmV4EyEHAMmakaz0goX2QOO4IHzj2Fg96TAjc8c652N6XzeO1GFOmUvbxKcnt2WoUoUCvk6vD179vCb3/yG3//+9wwZMoT4+HgmT54clmJX49Zbb2XJkiXk5+fz+eefc8stt7Bjxw6uu+66sMUQjUxagqjIDdN/AA8WtsOBB3ADHiDvB9jmjnCAbczj8UQ6hBZJ7RzPLdl9gxe7Gksehn8uhxN/zreJFpw01Pu7AZckmPR3XVdLcg65h3fMMccwePBgnn/+ec455xzeeOMNLr30Unbt2sWdd97Z7ACa4rLLLmP//v3cd9997Nmzh+OPP57XX3+do48+OizPL+1fvqvx/IgaFuB0wbwYHto08Q2Q07Nxn5ZF3sSJvPLKK5GORtqxkAteQUEBkydPrv19/PjxrF27lnPPPZevvvqKRYsWtUmADd1www3ccMMNYXkuiT7FHv8TAO3D94uImUIe0qxb7GoMGzaM999/n3Xr1rVmTCLNlhEXuIeXEePfD2LiF4KKhKrFf/4ZGRm89957rRGLSIvlxtf08Bq/8dtAXox/WYKRQ5oiIWqVbzw/8sgjW2M3Ii020OGdjZn3A9huN5bDgYW32DkTITOGz98Zp2g35L8BxV8Tl96d3uXq3UpgrVLwRNqTnI5wEm7OfXYFIy+eREact2dnQrEzZkizYDVM/1PtopuWZfG42wNLV0POuEhHJ+1UjJ/REPhp7TyTDLBsBj/7JM8kwbxOZhQ7oN76hjGraLe32HlscHvAY2O5Pd5zt3l/gm0lkY4wLEz8u4aWfagz4K9DRGJK/hs+v+jWu/C1Bc5VYQ9JooMKnohEl+Kv/X/vn334fhEfVPAMYOKKDCbmDIacw8vo6bOHBxy+9sT32rqxxtTXeEtyVsGTmFf0PczcBlP+z3tb1Pzvj5T2IHe8zx6e97vzbMg7K+whSXRQwZOYVlACg9+HBV/Bc197bwe/D0vNmNcQmwYeBc5bvN8U64iDuDhsR5y34Dlvgcw+kY5Q2ildliAxq/yI3kzf4l04uvY69MO3eVsg6wjIDHGN4mhhxJAmeC89yDreO0Gl+Gvs9O5cV7iSJ3RJggSggicxa+eQM72nenzUAAtwlsC8zHBH1baMOqeT2Qfm5QLgqa5mz8SXIhyQtHca0pSY9UNyj8CT+X4IazgiEmEqeBKzEg9+E3gyX2JYwwkLY4Y0RZpBBU9iVr8tawL28PJicG5DTA9pFu2HmathynPe26L9kY5IoozO4RnAxCWIbNum83clOId4J6gcXnLxp4Wkh8TehBWI4YJX8AlMX/nTAbSA+e+C80LIGWbsa9y0nKFloxgqeBLTcvp4Z2M6S7zn7DISvT27WCx2Matov7fYeXy80eWthKyj4ejkcEclUUgFT2JeZlLszcY0Sv7Hgb/V1/kx3DcmnBFJlNI5PAOYuASRiTlDjE5aKT7g89IS4PB02wNGHm8TcwYtLSYisSzjiMA9vIwjwheLRDUVPDFSUSnMXAdTVnpvi0ojHFArickeXu7wwD28vOHhjEaimM7hiXEKNsP01xtM+NsAzrMhZ2iEg2uhmBziGtjNOxszb6WP6bYXQmY3qK6OaIgSHVTwxChFpd5i53PC3+uQ1RcyU8MflwSRM8w7G9P5sfecXsYR3p5dZrdIRyZRRAVPjJK/OciEv80wLzuMAbWymBzSrJHZDeZpcWhpPp3DE6OEMOEvqsXkkKZIK1HBE6Nowp+IuVTwDGDiEkT+cs4dGmTCnyatRFZROczcAlM+9t4WlYf0ML3GzaGlxURCNDDVOxszr8EsTRvvdk1YiaCCHTB9U52ZmBbM3wbOEyAnPdLRSQxQwTOAiSsyBMo5Z6h3NqZzc50Jf0Njo9hF7Sf+onJvsfP59fSbICsVMrv4fbhe4+ZoSc4qeGKkzNTono0Zc/J34P/r6S1w7oB5Q8IelsQWncMTiSFR28Mr/gH/X15o6+vppVWohyfiQ9EeyF8Hxd9CRnfIzYaBvSMdVXBRO8SVkRi4hxeLX08vYaeCJ9JAwTqYvrjB3ImXwXkt5GRHOroYlZvunaDii21DniatSMtpSFOkjqI93mLnscHtqX+btxi27Y10hIFF7ZDmwC7e2ZhxgMOqf+s8IeCEFZFQqYcnUkf+uiBzJ9bCvCnhjip0UTukCd5LD7JSvRNUar+ePl3FTlqNCp5IHcXfBpk78W1444kpRdWQ/wMUuyHDAbmJMLDBW1BmF83GlDajgmcAE1dkaG7OGd2DzJ3o3vLY2lK77eEVfA/TDzb4TqYKcCZDTlKLd6/XuDlakrPO4YnUkZsduIeXNyas4cSGompvsfMAburf5h2EbfouOwkPFTyROgb29s7GjLPAEVf/1nktZPaKdIRRKP+HIN/JpGvsJDw0pGkAE5cgaknOOdmQNdg7QaXmOry8MdFR7NrlEFexO8h3Mrlb/BR6jZtDS4uJtLLMXqHNxizaDvkvQPEuyOgLuZfAwP5tH58/7bLgZTiCfCeTI5zRiMFU8ESaqeAFmD6zwQXqT4BzHuRcEpmY2uUn/txE7wQVX2wgT6uoSHjoHJ5IMxRt9xY7jwfc7vq3eTNhW3GkI2xHBnbwzsaMAxzUv3UmQ6Y+d0t46JUm0gz5Lxy+fMEHywLn8zDv9vDGBOEf0nQVQUU+uIvBkQGdcyF+oI+GOUmQ1dE7QaXmOry8RBU7CSu92kSaoXhXkAvUd4U3nhrhHNIsL4DvplPv2rpD8yHVCZ1zfDwgswPM6xq2+EQa0pCmSDNk9A3cw8voG954ws1VdLjY+bi2rjQPXH7WgRaJJBU8kWbIvSTIBeqTfN/3ZRH8fiZcPcV7+2VR28XYliryCTjzssIZzmhEQqOCZwATlyBq65wH9vfOxoyLA4ej/q1zHmRmNH7MsgIYNRgeWQAvPee9HTUYnlnaenGFa0jTXUzAa+vcxWEJ46en1GvcGC3JWefwRJop5xLIGuGdoFJzHV7eJN/F7ssiuHm6dxZnQ7/NgxOz4JjMNg85oPIi2JkPPxRDYgb0y4Uuviag4J2gEqiH58hoiwhFWkYFT6QFMjNCm425LD/wOb+nnfC7eb7v310Eq/Phm2LokQHjcuEoP4WouXYWwL+m17+m8Mv58Asn9Mtp3L5zrneCik82dM5r3fhEWkPUFLw//OEPvPbaa2zatImOHTty4MCBSIcUNUxcgqi95byjOPA5vx3Fvu9bXQAPNShEL8yHm51wZk7j9p7DXcjSbRbvL4cDxXBEBgzLhW5+imR5kbfY4flplLLm9l95kJoFnRv0PuMHemdjluZR/xsQbO/2+DD3Vtvb8Q4HE3MGQ5YWq6qqYtKkSYwaNQqnU2fEJbqkZwTu4aVnNN6+u8hb7GwfhWhhHvwsC/o0KCyWZTHUMw3nsMR6hei9+XCBE36Z0/h5dh7uffqqx5YFO5xwnI/eZ+cc6JjlnaBSex1eXviLnUioombSyty5c7nlllv4+c9/HulQRJpsam7gHt7lPoYAVwcZBn3Dx+e+I9zHcLZnMbbHwnYfLpaHb1/Kg/0+Lhf4oThwbD8U+74PvMXtiHnQ7RnvrYqdtGdR08NrjsrKSiorK2t/P3jwIAAulwuXyxW0a1x3NlCgtqG2a27blu6zuroa27Zrb0N5/vaeU7C2dXNurX0Gaxuo3dH94Y9PwK3XOOoNT9o2/PEJD+kZNnVCxbZt9v7HgW1b+JwdYtvs3W7jcv30TQPV1dWcYOXid/qkZbPxCQ9j/+CpF2tCehyWZWH7eB7LsklIt6mu9jHbhrb5N23OPt1ud6Pj7a9tW7/2wrXPmtd4a76XNaVtpP6eAh3jYGK64M2bN4+5c+c22j516lTi4+Oj/sCHuk/btiksLGTixIkxk1OwtnVzbq19BmsbSruhp/bmm53jqPyhBwmJ39AjfQ3PrtzDsysbt/V8MQ3si/AuPFmfx/bw7sa/897EJ2u3ud1uulZchb/pkx63h1effpeHtyyoF2tyeW8ucz+Ot7T+tN3GxuO2+Z/C6zg4cU/A3EPNP5S2zd1nw+Ptr22sFIe6r/FYyaluW3/tqqqqAj4+EMuO4IUcc+bM8VmQ6iosLGTEiBG1vy9dupSbb745pEkrvnp4/fr1o6ysjOTk5GbHHW2qq6uZOHEir7zySqRDCZtYyHl3EVwz2Dsc2ZAVB3/ZWv8cXkVFBZO6LWZ45W+I8/FZ1nLA6NvhTB/n43Yu9U5Qadj79DdLs72JhePdVCbmDFBaWkq3bt2a9T4e0R7ejBkzmDx5csA2GRkZzd5/QkICCQkJzX68SCQdNdA7G3Ph4UJUMwHFtr3bG05YAfisw1MMr/ztT43rsmGYn8sF+uV4Z2PucP50HV56XuPZmSLRLKIFLy0tjbS0tEiGYAQTV2SIlZzPzPHOxnzD+dN1eOPzfBc7gIPxxbwWdw3ns6TR5QIXOKFbgALWOdP3bMxoECvHuylMzBkMWWllx44dlJaWsmPHDtxuN5s2bQIgMzOTLl26RDY4kTbUJxOuakIh+r+4v/Lyxw/z+TNJP12Hlxe42ImYIGoK3qxZs3jyyZ9O0P/yl78EYO3atWRnZ0coKpH26cgBts9zdSImi5rr8JYuXVrbha/7o2IXnIkrMpiYM4T/C2DbCxOPt4k5Q8tWWomagiciItISKngiImIEFTyRGGLqkKZIKFTwRGKIied0REKlgiciIkZQwROJIRrSFPFPBU8khmhIU8Q/FTwDmLgEkYk5g7kFz8TjbWLO0LJRDBU8ERExggqeiIgYQQXPACYuQWRizmDupBUTj7eJOYOWFhMREQlKBU8khpjawxMJhQqeSAwxcYhLJFQqeCIiYgQVPJEYoiFNEf9U8ERiiIY0RfxTwRMRESOo4BnAxCWITMwZzO3hmXi8TcwZtLSYiIhIUCp4BjBxRQYTcwZzJ62YeLxNzBm00oqIiEhQKngiMcTUHp5IKFTwRGKIiUNcIqFSwRMRESOo4InEEA1pivingicSQzSkKeKfCp6IiBhBBc8AJq7IYGLOYG4Pz8TjbWLOoJVWREREglLBExERI6jgGcDEJYhMzBnMnaVp4vE2MWfQ0mIicpipBU8kFCp4IjHExE/8IqFSwRMRESOo4InEEA1pivingicSQzSkKeKfCp6IiBhBBU9ERIyggmcAE5cgMjFnMHdI08TjbWLOoKXFREREglLBExERI6jgGcDEJYhMzBnA4/FEOoSIMPF4m5gzaGkxETnMxDdAkVCp4ImIiBFU8ERiiImz9kRCpYInEkM0pCninwqeiIgYQQVPJIZoSFPEPxU8A5i4IoOJOQPExZn5J23i8TYxZ9BKKyIiIkFFRcErLi4mLy+P/v37k5iYyIABA5g9ezZVVVWRDk1ERKJEh0gHEIovvvgCj8fD4sWLyczM5N///jdXX301FRUVPPDAA5EOr90zcUUGE3MGc8/hmXi8TcwZWjYTOSoK3llnncVZZ51V+/sxxxzD1q1beeyxx1TwREQkJFFR8HwpKysjNTU1YJvKykoqKytrfz948CAALpcLl8sV9JNC3U/LgdqG2q65bVu6z+rqamzbrr0N5fnbe07B2tbNubX2GaxtW+cUrF11dTXJyclUVlbidrvr5d7c5490TqHu0+12Nzre/tpGS07B2ta8xlvzvawpbSP19xToGAcTlQXvyy+/5OGHH+bBBx8M2G7evHnMnTu30fapU6cSHx8f9Qc+1H3atk1hYSETJ06MmZyCta2bc2vtM1jbSL/puN1uvv32W6qqqpg8eTIOh6PFzx/pnJqyz4bH21/baMop2D5rco6VnOq29deuRXM37AiaPXu2DQT8KSwsrPeY3bt325mZmXZeXl7Q/f/44492WVlZ7c/OnTttwC4rK2urlNoll8tln3vuuZEOI6xMzLm8vNxOSUmxO3ToYJeXl0c6nLAy8XibmLNt2/b+/fub/T4e0R7ejBkzmDx5csA2GRkZtf9fUlLCmDFjGDVqFE888UTQ/SckJJCQkNDSMEVEJAZEtOClpaWRlpYWUtvdu3czZswYhg8fTkFBgbEX2IoEYhs6S1MkFFFxDq+kpITs7GzS09N54IEH+Pbbb2vv69WrVwQjE2lfTJymLhKqqCh4q1evZtu2bWzbto2+ffvWu0+faIOzDVyCyMScwdyCZ+LxNjFnMGBpsZycnNqD2/BHREQkFFFR8ERERFpKBc8AJi5BZGLOYO4Qv4nH28ScoWXD9ip4IiJiBBU8kRhiag9PJBQqeCIxxMQhLpFQqeCJiIgRVPBEYoiGNEX8U8ETiSEa0hTxTwVPRESMoIJnABNXpTExZzC3h2fi8TYxZzBgaTEREZGWUsEzgIkrMpiYM5g7acXE421izqCVVkRERIJSwROJIab28ERCoYInEkNMHOISCZUKnoiIGEEFTySGaEhTxD8VPJEYoiFNEf9U8ERExAgqeAYwcUUGE3MGc3t4Jh5vE3MGrbQiIiISlAqeiIgYQQXPACYuQWRizmDuLE0Tj7eJOYOWFhORw0wteCKhUMETiSEmfuIXCZUKnoiIGEEFTySGaEhTxD8VPJEYoiFNEf9U8ERExAgqeCIiYgQVPAOYuASRiTmDuUOaJh5vE3MGLS0mIiISlAqeiIgYQQXPACYuQWRizgAejyfSIUSEicfbxJxBS4uJyGEmvgGKhEoFT0REjKCCJxJDTJy1JxIqFTyRGKIhTRH/VPBERMQIKngiMURDmiL+qeAZwMQVGUzMGSAuzsw/aROPt4k5g1ZaERERCUoFT0REjKCCZwATV2QwMWcw9xyeicfbxJxBK62IiIgEpYInIiJGUMETiSGmDmmKhEIFTySGmHhORyRUKngiImIEFTyRGKIhTRH/oqbgnX/++aSnp9OpUyd69+7NFVdcQUlJSaTDEmlXNKQp4l/UFLwxY8bw3HPPsXXrVl588UW+/PJLLrnkkkiHFRVMXILIxJzB3IJn4vE2MWdo2ShGh1aMo03dcssttf9/9NFHc9ddd3HhhRficrmIj4+PYGQiIhINoqbg1VVaWsrTTz/NySefHLDYVVZWUllZWft7WVlZ7eNdLlfQT8N1P0kEahtqu+a2bek+XS4XVVVVlJaWxkxOwdrWzbm19hmsbVvnFKzd999/T5cuXfjxxx/57rvv6r32m/v8kc4p1H1WV1c3Ot7+2kZLTsHa1rzG9+/fHzM51W3rr913333XaJ8hs6PIHXfcYSclJdmAfdJJJ9n79u0L2H727Nk2oB/96Ec/+omxny+//LLJNcSy7cgNAs+ZM4e5c+cGbFNYWMiIESMA2LdvH6WlpXz11VfMnTuXlJQUXn31Vb+fBBr28A4cOMDRRx/Njh07SElJab1E2rmDBw/Sr18/du7cSXJycqTDCQsTcwblbVLeJuYM3pG69PR0vvvuO4444ogmPTaiBW/fvn3s27cvYJuMjAw6derUaPuuXbvo168f77//PqNGjQrp+Q4ePEhKSgplZWVGvUBMzNvEnEF5m5S3iTlDy/KO6Dm8tLQ00tLSmvXYmjrd8DyFiIiIL1ExaeWjjz7io48+IisriyOPPJL//Oc/zJo1iwEDBoTcuxMREbNFxXV4iYmJ/P3vf+f0009n0KBB5Obmcvzxx7N+/XoSEhJC3k9CQgKzZ89u0mNigYl5m5gzKG+T8jYxZ2hZ3hE9hyciIhIuUdHDExERaSkVPBERMYIKnoiIGEEFT0REjKCCJyIiRjC24Jn4/XrFxcXk5eXRv39/EhMTGTBgALNnz6aqqirSobW5P/zhD5x88skkJSU1eTmiaLFo0SL69+9Pp06dGD58OO+8806kQ2pzb7/9Nueddx59+vTBsixWrlwZ6ZDa3Lx58xg5ciRdu3alR48eXHjhhWzdujXSYbWpxx57jKFDh5KcnExycjKjRo3iH//4R5P3Y2zBM/H79b744gs8Hg+LFy/ms88+409/+hOPP/44d999d6RDa3NVVVVMmjSJ66+/PtKhtIlnn32Wm2++mXvuuYdPP/2UU045hQkTJrBjx45Ih9amKioq+MUvfsEjjzwS6VDCZv369dx4441s2LCBNWvWUF1dzbhx46ioqIh0aG2mb9++3H///WzcuJGNGzcyduxYLrjgAj777LOm7ajJy03HqJdeesm2LMuuqqqKdChhNX/+fLt///6RDiNsCgoK7JSUlEiH0ep+9atf2dddd129bYMHD7bvuuuuCEUUfoC9YsWKSIcRdt98840N2OvXr490KGF15JFH2kuWLGnSY4zt4dUV6vfrxaKysjJSU1MjHYa0QFVVFR9//DHjxo2rt33cuHG8//77EYpKwqXmez5N+Tt2u90sX76cioqKJi8taXTBu/POO+ncuTPdunVjx44dvPTSS5EOKay+/PJLHn74Ya677rpIhyItsG/fPtxuNz179qy3vWfPnuzduzdCUUk42LbNrbfeSlZWFscff3ykw2lT//d//0eXLl1ISEjguuuuY8WKFQwZMqRJ+4ipgjdnzhwsywr4s3Hjxtr2t99+O59++imrV6/G4XBw5ZVXNu9bdCOsqXkDlJSUcNZZZzFp0iSmT58eochbpjl5x7KG3wtp23bQb5eW6DZjxgw2b97MM888E+lQ2tygQYPYtGkTGzZs4Prrr2fatGls2bKlSfuIim9LCNWMGTOYPHlywDYZGRm1/1/z9UTHHnssxx13HP369WPDhg1R9w0MTc27pKSEMWPGMGrUKJ544ok2jq7tNDXvWJWWlobD4WjUm/vmm28a9fokdtx00028/PLLvP322/Tt2zfS4bS5jh07kpmZCcCIESMoLCzkoYceYvHixSHvI6YKnqnfr9eUvHfv3s2YMWMYPnw4BQUFxMVFbye/Jcc7lnTs2JHhw4ezZs0aJk6cWLt9zZo1XHDBBRGMTNqCbdvcdNNNrFixgnXr1tG/f/9IhxQRtm03+f06pgpeqEz9fr2SkhKys7NJT0/ngQce4Ntvv629r1evXhGMrO3t2LGD0tJSduzYgdvtZtOmTQBkZmbSpUuXyAbXCm699VauuOIKRowYUdtz37FjR8yfny0vL2fbtm21v2/fvp1NmzaRmppKenp6BCNrOzfeeCPLli3jpZdeomvXrrU9+5SUFBITEyMcXdu4++67mTBhAv369ePQoUMsX76cdevWsWrVqqbtqNXnikaBzZs322PGjLFTU1PthIQEOyMjw77uuuvsXbt2RTq0NlVQUGADPn9i3bRp03zmvXbt2kiH1moeffRR++ijj7Y7duxoDxs2zIhp6mvXrvV5XKdNmxbp0NqMv7/hgoKCSIfWZnJzc2tf2927d7dPP/10e/Xq1U3ej74PT0REjBC9J3BERESaQAVPRESMoIInIiJGUMETEREjqOCJiIgRVPBERMQIKngiImIEFTwRETGCCp6IiBhBBU8kSj3zzDN06tSJ3bt3126bPn06Q4cOrf1SUBH5iZYWE4lStm1zwgkncMopp/DII48wd+5clixZwoYNGzjqqKMiHZ5Iu2PktyWIxALLsvjDH/7AJZdcQp8+fXjooYd45513aovdxIkTWbduHaeffjovvPBChKMViTz18ESi3LBhw/jss89YvXo1p512Wu32tWvXUl5ezpNPPqmCJ4LO4YlEtTfeeIMvvvgCt9vd6NvNx4wZQ9euXSMUmUj7o4InEqU++eQTJk2axOLFixk/fjy/+93vIh2SSLumc3giUai4uJhzzjmHu+66iyuuuIIhQ4YwcuRIPv74Y4YPHx7p8ETaJfXwRKJMaWkpEyZM4Pzzz+fuu+8GYPjw4Zx33nncc889EY5OpP1SD08kyqSmpvL555832v7SSy9FIBqR6KFZmiIxavz48XzyySdUVFSQmprKihUrGDlyZKTDEokYFTwRETGCzuGJiIgRVPBERMQIKngiImIEFTwRETGCCp6IiBhBBU9ERIyggiciIkZQwRMRESOo4ImIiBFU8ERExAgqeCIiYoT/D7bPwy7oI6y3AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(X_grid, X_circle, X_vec, 'Original Grid and Points')  # 绘制原始图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "513a35e1-4449-4d44-8092-0288a7f7c7f7",
   "metadata": {},
   "source": [
    "## 定义变换矩阵 A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b4660c50-468e-4b7a-a2e2-1be6d23aa212",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1.6250, 0.6495],\n",
    "              [0.6495, 0.8750]])  # 定义矩阵 A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42d053d3-e73d-4352-83cb-2d916a5eaf32",
   "metadata": {},
   "source": [
    "## 绘制应用 A 后的变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "18d6d66e-7fb9-4bdc-b9b4-fa45f5340ace",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UKQgICChxbL28QHc4OSEEN2/elKq5mTNn4tixY6hatSrlfVGNJuHk8ujC4VGp5mR5+fIlAgICCk0LsPw3LeDo6IiKFSvCx8eHVXNKwjo8CsjOzkZgYCDc3Nzw5s0bBAcHsxkgZKAznDw5ORmenp44duxYITWnL6mm1AknLwltKh2q1Zws2dnZWLRoETw8PNjqEHLs3bsX7dq1g4+PjzRZfFlVc1TDOjwNeP78ObhcLl6/fo0JEyagQoUKuHz5MuUJW/UdqsPJJXNzfD4fKSkpjJ6bKwlVw8mZgEgkwunTp+Hm5oZKlSrBzMyMEjUnj42NDVasWIHGjRtT2q4+k5OTg507d+Lo0aMYPXo0TE1N0b17d61XMddn2F9KRSRqzs/PDz///DMsLS3RuXNnrFy5EpaWlqyzk6O0cHJVkFdz69ev19vfW9lwclWha0jz48ePEAgEuHLlCoYNG4bDhw/TFkTi7+8PIyMjDB8+nJb29Q1JIefHjx/j48ePuHnzJpo1a6Y3oxhMgnV4SvLs2TNwuVxERUVhypQpCAwMlD6oymo4uaZQEU4ur+bmzJmjl2pOnu3bt5cYTq4uVA5pKlJzdNebe/v2Ldzc3PRK9dKBfOkvc3NzfPr0CVu3bkWzZs10bZ7ewjq8EsjOzkZAQAD8/f0LqTlZylo4OZVoEk5eltScPFevXsWrV69ga2ura1MU8uHDB7i4uGhFzcmSm5sLa2tr8Hg8vX+hUZfiCjk7OTmhR48e6N27t65N1GtYh6cAWTU3derUQmpOFirDycsayoaTyyK7bi4tLU1v5+ZKIiEhAfb29oyrDqELNSfPqlWrsHDhQjRv3lxrfTKB0go5P3r0CBcuXEBAQIAOrSwbsA7vO1lZWQgMDIS/vz9atGgBCwuLUpMaUxlOTifaDlV/+fIlAgMDERYWptT2SUlJ8PT0xPHjx9G7d2/Y29trrOZ0vR5NEZJw8t27d9MWUaeqE/3w4YN0bm748OFwcnJSq16jpkiulXHjxqm1PxPPd2koU8g5PT0d//zzD/z9/Yu8fOjjMVMBm1pMA549ewZnZ2e8efOmRDUnD9Xh5GUFZcPJCSG4fv06+Hx+mVVz8uzduxcDBgzQeXJwkUiEU6dOwc3NDVWqVIGZmRnWr1+vM8X5/v17ODk5lYtpAVUKORNCsGjRImzYsAH16tXTsqVlk3Lp8LKyshASEgJ/f3+0bNlSKTUniz6Gk2uLf/75p8Rwcnk1t2HDBhgbG2vXSB1w584d3L17Fz4+PjqzQaLmrl69iuHDh+PIkSM6UXOyyFaHqFy5sk5toRN1Cjm7urqiTZs2+P3337VkpX7w7ds3tfctlw5v9uzZmDlzJoKCglQOCacrnJxOtPXmHhAQgFq1ahUJJyeE4Nq1a+Dz+UhPT9dKpCWT5sdSUlKwevXqQmmg6EIsFhf6m2lqTp5169Zh3rx5GpdlYsrxyKJJIefnz58jIiICISEhxW7DxGOmG7FYDBsbG7X3L5cOLzg4WO36T3SFk+s7b9++haurayHVm5SUBA8PDxw/fhx9+/aFg4NDuVBzshBCYG1tjW3btqF27dq09yd5CH748AF+fn6MUnPynD59GqmpqZg6daquTaEUSSFnVdScLFlZWVi6dCm8vb3Z6hByODo6YsiQITh16pR6DZByRGpqKgFAUlNT1dr/ypUrZM6cOUQsFlNsGb0IhUIiFAppaz8nJ4cMHTqUxMTEELFYLP2dJkyYQEJDQ0leXh5tfRcH3cesLIcPHya7du3SSl8pKSmkWrVqpEKFCmTatGnk4sWLjL1WP378SAYNGkSysrIoaU/X5zsrK4t4enqSkSNHEmtra/LgwQO127KwsCDnz58vdTtdH7O2uXbtGpk1axZJSEhQ+zleLhWeOjA1nJwJrF69GrNnz0ZoaGi5VnPyPHz4UCvh5HFxcRAIBLh8+TJEIhGqVKkCgUDA2CF3kUgES0tLHDp0SC+Se5eEpJDzy5cvMWXKFI1Lf3l7e6Nhw4YYNGgQhVbqP4mJiVi3bh3CwsI0yjDDOjwlIFoIJ9dHCCHYvn07zpw5g9jYWMyZMwenT59mc/vhv3DygIAAWoal8vPzcerUKbi7u6Nq1aowMzPDihUr0KRJE8r7oppNmzZh6tSpaNu2ra5NUQv5Qs4WFhaURN6+fv0avr6+Si/nKS9Inr+7du2CWCwGj8dTuy32yaQETAknZwqJiYnw8PBAcHAw4uPjcfr0acavRdQm5Ht1CAcHB8rDySVq7tq1axgxYgSOHj0q7SMzM5PSvujgwoULiI2NxYYNG3RtispI1BwdhZxzcnKwcOFCuLm5sS+Mcuzbtw9NmjTBoUOHkJycrPZaTYB1eKXChHByJkAIwdWrV8Hn85GZmYmZM2eiZs2aOHfunMYRdmUNFxcX/PLLL5SFk0vUnJubG6pVqwYzMzPY29srHFonDF6M/PXrV2zevFmvlvPIqzm6CjmvWLECy5cvx08//UR52/pKcnIytmzZAk9PT5iammLx4sVo0aIFkpKS1G6TdXgloM1wcjrR5CEoUXMnTpxAv379sGnTJjRv3hy2traUhJPTha4e/M+ePSs1nFxZ4uLiwOfzcf36dYwYMQLOzs6lKkamRvVJlvPs27ePMlUkC9XnW1L6SxuFnIOCglCtWjWMHDlSpf2Y/HKjLkSmkPPXr1/x/v17PH78GA0bNiy0jbqwDq8YiJbDyZmEvJqTn5s7c+YMUlJSylw4uaZkZmZKw8nVLVqan5+PkydPwt3dHdWrV4eZmRk2bNig1y9cQEE4+ciRI9GpUyddm1IsktJf/v7+MDY2hoWFBS1qTpZ3795BIBDoleqlg+TkZHh5eSEiIgI9e/bE2rVrsW7dOvB4vELOTlNYh1cMR44cKXfZyYtTc7LEx8dj586d5SINlKosW7YMtra2at2gsbGxEAgEuH79OkaOHKmUmtMXrl+/jmfPnsHT01PXpihEtpAz3WpOlry8PFhbW8PZ2blMp9QrDlk1J1/I+ejRo+jSpQv69u1LaZ+sw1NAWctOXpI6kFVzGRkZmDt3brGRliKRCFZWVnoRTq5tReTl5YWGDRti8ODBSu9Dh5pj2jCXbDg5nedE1bZ1oebksbW1xfz589VevqOvqr+00l+PHz/G2bNnERQUpHB/TY6bdXhylJSdvCyRmJgId3d3nDx5Er/99ptCNSfP5s2bMWXKFL0NJ6cLSTh5eHi4UtuXZTUniyScfOfOnWpnNqIaXak5eY4dO4b8/HxMmDBB633rAiJXyLm4ZPEZGRlYvnw5bc9f1uHJQMp4dnJCCK5cuQI+n4+srKwS1Zw8Fy9exPv372Fvb68FS/UHSTi5q6trib+jvJozNzcvE3NzJbF//378/vvv6N69u07tkKg5Pz+/Ygs5a5O4uDgcPHiwXEwLqFLImRCCxYsXw97enrY0eKzDk6GsZidPSEiAp6cnzpw5g99++w1btmxBs2bNlN5fEk6urIIpT6xYsQLLli0rdsF3bGws+Hw+bty4gVGjRoHL5aJu3bq02cOUIc27d+/i1q1b8PX11ZkNyhZy1iaSotFOTk5ltjqEvJpTNlm8u7s7fv75Z/z555+02cY6vO88f/4c4eHhlISTMwFZNZeZmYnZs2dj+fLlKi9qFYvFsLKywt69e2kJJ9dngoKCULVqVYwaNarQ5/n5+Thx4gQ8PDykas7BwUErao4JijE1NRWrVq1CcHCw1u1Rp5CzNrG3t8ecOXPQqlUrXZtCOaqoOXkiIyMREhKC0NBQWm1kHR4KbpIlS5ZoFE7OFBISEuDh4SGdm9uyZYu0Np06GRx27tyJESNGMDqcXBe8e/cOfD6/UDj5+/fvIRAItKbmmAghBAsWLMDWrVvxww8/aK3fZ8+egc/n4927d5gyZQoj1Jw8Z8+eRWJiIqZPn65rUyiDUFDIWfL89fT0pP35yzo8aBZOzgRk1Vx2dnaRuTl1k63euHEDT58+ZWw4ua6QDSc3MDBAeHg43N3dUaNGDa2qOUXoekjT2dkZXbp0QZ8+fWjvS1bNGRsbw8zMTOfzhcXx6dMnODo6lpn1dvKFnO3t7ZVWc/LY2Nhg1apVaNSoEcVWFqXcOzxvb280aNBApXByppCQkAB3d3ecOnVKrbm5kkhMTMTatWtpDyfXR2xtbTFx4kQIBALcvHkTo0aNAo/HY4Sa0+W5Ki2cnCqePXsGZ2dnvHnzRjo3x+T5MMlyngMHDqBatWq6NkdtqFBz8vj6+qJu3boYMmQIhZaWgFqFifQU+Xp4r169IiNHjtSrmlJisZhcvHiRzJo1i0yaNIlERESUan9eXp5KNenEYjGZPHkyuXfvnqbm6gxVj1kZhEIhsbOzIy1atCBz5swhV65cYVS9uYyMDFK7dm1Su3ZtkpGRodW+09PTycCBA8nXr19paT8zM5O4urqSESNGkEWLFpHHjx8X+p6O800VGzduJK6urpS3q61jTkxMJPv27SODBw8mdnZ2JDo6mpJ2X79+TUaMGKHy85eth6cGyoaTMwVZNde/f39K1Zw8TAknZwrv378Hn8/HxYsX8e3bN1y5coVN8isD+R5Ovn79esrDyZ8+fQoul4u3b99i6tSp0ryT+sLly5fx7t07rF27VtemqAQhBNeuXQOfz0d6errSkZbKkpubi4ULF0IgEGj1+cv8Jz1NSLKTM7l+GCEEly9fBp/PR05ODubOnYulS5fSeoHcvXsXN27cgL+/P2196ANCoVAaaVmzZk2YmJjg/v37cHV1ZZ2dHO7u7mjRogVl4eRZWVkICAhAQEAAWrZsCQsLC70Mmvr27Rs2btyoV0Wjk5KS4OHhQXsh55UrV2Lx4sVo2rQp5W2XRLl0eGFhYWplJ9cWCQkJcHNzw6lTp/D7779j27ZtGl0Yyt5sqampWLlypU7CyalGXftjYmKkc3OjR48Gn89HnTp1YGdnh9mzZ6N169YUW0otRMtBK1SGk2ui5ph2vUqW8+zZs4e25TxUHbMiNXfq1Cna8nuGhoaiQoUKGDNmjFr7s6nFVMTT0xMnT57UtRmFIITg0qVLEAgEyMnJgYmJCZYtW6Y1uU++V4fYunUr6tSpo5U+mYK8mrOwsMDGjRulN9bZs2eRkJCAGTNm6NhSZkFFOLlEzfn7+6NVq1awtLREx44dKbZU++zevRtDhw5l1BpAebSl5mSJiYmBs7OzzqJVy6XD27NnD2Oyk3/79g3u7u44ffo0JWpOXSTh5FRnJ2cyMTEx4PP5uH37diE1J8unT5+wY8cOvUkDpU2Ft3z5crXDyZ8+fQpnZ2e8e/cO06ZNQ3BwsF7NzZXEzZs38ejRI3h5eenalCLIqzlV0gtqilAoxPz583HkyBFUqlSJ9v4UUS4dXmlJkulG12pOHm2FkzMBoVCI48ePw8PDA0ZGRjA3N8emTZsUDpNIwskPHjyoNw9jbQ3t+fj4oF69eiqFk2dmZkrn5lq3bg0rK6syoeZkSU5Ohp2dHUJDQxk1zCpb+qtv377YuHGj1p+DdnZ2MDc3V3u9HhWUS4enK5ii5mShOzs5U5BXcwKBoNSh261bt2LChAlo3769lqzUD6KioqTFOpXhyZMn4HK5ZVLNyUK+V4fYsWMHjIyMdG1OqYWctcnJkyeRlZWFyZMna71vWViHRzMSNcfn85GbmwsTExMsX76cESnMiBayk+sSoVCIY8eOKaXm5Ll8+TLevn2rl+HkdJKTk4MFCxbAxcWlxAdneVBz8hw6dAh9+/ZFz549dWqHMoWctcmHDx+wd+9eRkwL6JXD27ZtG0JCQvDy5UtUrVoV/fr1w44dO/DLL7/o2rQifP36Varm/vjjD+zYsYNxSyC0kZ1cF8TExIDL5eLOnTsYM2aMUmpOlm/fvsHBwUGvwskl0G3vypUrsWTJkmJHJp48eQJnZ2dER0eXaTUnz/3793H16lWdLedhkpqTRVId4vDhw6hSpYpObQH0zOFdvnwZCxcuRM+ePZGfnw87OzsMHToUkZGRjEgUSwjBxYsXIRAIkJeXBxMTE9jY2DBCzcmjrezk2kJ2bq527dowMTGBg4ODysFJstUhatasSZO1+klISAgqVqxYJJw8MzMT/v7+CAwMRJs2bWBtbY1ff/1VR1Zqn7S0NPz7778ICgrS+gtSYmIifHx8cPLkSUaoOXkcHBwwc+ZMtGnTRtemFKBybhYG8fXrVwKAXL58Want5VOLUcWXL1+Io6MjGTRoEHFwcCBxcXGUtq8p8imIMjMzyaBBg0h8fLwOraKGd+/ekTVr1pDBgweT/fv3k8TEREKI+mmXHB0dyZEjR6g2UyvQmVrs3bt3ZOjQoSQ3N1f62aNHj8iCBQvIiBEjiLu7O8nMzKS0T1XQVWoxsVhMZs2aRa5du6bVPi9dukRmzpxJxo8fT8LDwxmZHvHcuXPE3Nyc8nbLbWqx1NRUACh2uCo3Nxe5ubnSv9PS0gAUqAGhUFjq2xiRmQ+R31YsFuPy5ctwcXFBXl4e5syZg8WLF5daoaCkNovbVhM7ZW3hcDgghGDZsmX4559/UL9+fUrtVGVbTdqUqDlvb28YGRnB1NQU9vb24HA44HA4yM/PL3TMytp58+ZNPHjwAB4eHhAKhVo9JnW3ld0uPz8ftWrVAlAQYSp/btU9T3l5eZg/fz4OHTqE7OxsuLu7Izg4GK1bt4a5ublUzUl+eyqPSVk7FZ3vko5JmTaV2ZbP56Nt27bo1asXJcde0raSubnTp0+jX79+sLe3R9OmTZWqikL3tSe/3efPn7F161aEhoYiPz+f0meEutVfAD0b0pSFEAIbGxv079+/2OGTbdu2wcHBgdJ+v379Ck9PT5w9e1Yaacn0VFOyF46fnx/q1Kmjl9UhoqOj4eLigrt370rrzdWpU0dhoIaqQ0vJyclYv369dFhKUZv6AB12r1u3DgMHDsSePXvw/v17ab25qlWrMuZ30sVc69OnT3Hq1CkEBATQ1gf5PjcnEAiQnZ2N2bNn48SJE6hQoYJGD346EYlEWLBgAfbu3UvLVJNG51plTcgQFixYQJo3b17i8GFOTg5JTU2V/hcXF6eWFBaJROT8+fNkxowZZPLkyeT48eMkPz9f00PQGkKhkAiFQrWzk+uSvLw8EhwcTMaNG0dMTEzItWvXlKpQIDlmZRCLxWTq1Knkzp07mpqrUzIyMoiRkRExMjKiZEgzIyODLFmyhDRr1owsWbKEPHv2jAIr6UGV800FGRkZZODAgeTLly+0tP/t2zeye/duMmjQILJ+/Xry/v37Itto+5iVZfPmzYTP59PWfmJiYvka0ly8eDEiIiJw5cqVEiMfK1eurFGdrK9fv8LNzQ1nzpzBn3/+CUdHR8ZFWiqLrrKTq0t0dDR4PB7u3r2LsWPHwtXVlbYK2kwJJ6cCQoHievz4MZydnfHy5Ut8+fIFjx490mr1cn1gyZIlWLt2LX788UfK2iSlFHLWB65evYpXr15hzZo1ujZFIfrzS+K/dWOhoaG4dOkSLSv2xWKxNNJSKBRi3rx5+OeffxgZaakKq1ev1kl2clUQCoWIiIiAp6cnfvjhB1hYWGDLli20DlfpOpycatT9rTIyMqSRlm3btoWVlRXWrFmD0NBQ1tnJ4eHhgaZNm2LAgAGUtKfN0l90kpCQAHt7e0Yv59Erh7dw4UL4+PggPDwcNWvWxOfPnwEARkZGqFq1qkZty6q5v/76Czt37mT83JyyhIWFaZSdnG7evXsHPp+vFTUniy7DyZnCo0ePwOVy8f79e0yfPh2hoaGoWrUq1q1bx6xwcobw8uVLBAYGIiwsTKN2yPfSX5K5OW2U/qITyXKe3bt3M3s5D8XDq7QCQOF/ylYTll+WIDs3N2XKFHLixAm9mptThujoaDJ06FCdhowrIi8vjwQFBUnn5q5fv05p9fDS5jd0EU5ONxkZGaRWrVqkVq1aJc7hpaenEz6fT4YNG0aWLl1aZG6OrnByOtHGfFZWVhYZPHgw+fjxo9ptfPv2jezatYsMGjSI2NvbK5ybUxYmzeHt2rWLHDp0SCt9lZs5PEJRRNi3b99w5MgRnD17tsypOVkk2ckPHTqks+zk8uhKzcnD5/PRoUMH/Pbbb1rvm05KUqqPHj2Cs7MzYmNjC6k5WT5//oxt27bprHwLk/nnn3+wYsUKNG7cWKX9iA4KOWuT27dv4+7du/D19dW1KaVSNn5xFVmxYgUsLCywYsUKvZ+bKwkmZCcHCs/N1alTRytzcyXx9OlTnDx5EsHBwTrpX5tkZGTAz88PQUFBaNeuHRYvXlxsMmxJdYgDBw4wInMRkwgICICRkRGGDRum9D6SQs5MShZPNcnJyVi9ejXjqkMUR7l0eO7u7tIFumUV2ezksouotcm7d+/A4/Fw7949jBs3TqtqrrjRgMzMTCxbtgy+vr5lsjqE5KHz+PFjeHp6IjY2FjNmzFCo5uTZvn07xo4diw4dOmjDVEqhavRHEW/fvoWbmxvCw8OVskNbpb/oPGZl+7e2tsb27dtRu3ZtrfarLuXS4ZV1dJmdXCgUIjw8HF5eXlI1t3XrVsa8/dERTs4UMjIykJubC6FQCB8fnxLVnDxMDyfXFbm5uViwYAF4PF6JeVmZWPqLbpycnNCzZ0/07t1b16YoDevwyhi6yk7+9u1b8Pl8qZpzc3PT6lufMri7u1MaTs4UHj58CC6Xi5iYGHA4HFSvXh07duxQelhSH8LJdcXq1auxcOFChcsEZNVcbm4u5s6dy5jSX3Tz8OFDXLhwAYGBgbo2RSVYh1fG2LhxY5FwcroeYnl5eYiIiGCkmpO3QRJOrsywlD4gPze3ZMkSNGvWTOXgK70JJy8FOq45SeDO2LFjC30ur+a2b9+uk4QUurrP0tPT8c8//yAgIEDr0wIxMTE4dOiQ2vuzDq8M8b///Q+fPn3Cxo0bae1HH9ScLNnZ2Vi0aBE8PDz0/u1boubi4uIwY8YMhIWFSZV8ZmamyvMbe/fuxcCBA9G1a1c6zNVbYmNjcfjwYem0gLyaY1IhZ21CCMHChQvh4OCAevXqaaVP2dJfRkZGmDJlCnbv3q1WW6zDKyN8+fIFW7dupS2cXKLmPD09Ua9ePUapudKwsbFRK5ycKWRkZMDX1xdBQUFo3749lixZgnbt2incVpXzoU/h5NpEspzHyckJKSkpcHd3x5kzZ/DHH3/oTM0xBRcXF/zyyy/4/fffae8rJiYGfD4ft2/fxujRo6WFnJOSktRuk3V4ZQCxWAxLS0tawsnfvn0LHo+H+/fvY/z48XB3d2e0mpPH398fRkZGGD58uK5NUZkHDx6Ay+Xiw4cPmDFjBsLDwymbl9W3cHJtsnbtWvTo0QPr169nfCFnbfLs2TNEREQgJCSEtj7kCzmbm5tj06ZNlF2jrMMrA1AdTp6XlyeNtJSouW3btundg1ESTq5Pi6jT09Ph5+eH4OBgtG/fHkuXLi1WzSlCmSFNXYWTM52vX79izZo1OH36NCwtLbFjx45yreZkyczMxNKlS+Ht7U2L44+JiQGPx8OdO3cwZswYqZqjGtbh6TmScHJbW1uN23rz5g34fD4ePHiAcePG6Z2akyU3NxeLFi0Cn88vMZycKcirOdm5OVVQ5qVEH8PJ6UIsFkvn5lJTU/Hx40e8fPkSNWrU0LVpjGLZsmWwtbVFw4YNKWtTKBTi2LFj8PT0lKq5zZs30/pizTo8PYaKcPKyoubksbW1hbW1NZo3b65rU4pFouaCgoLQoUMHLFu2DG3btqW1T30NJ6caSbL4s2fP4s8//8TWrVuxcOFC+Pr6ss5ODi8vLzRs2JCyotHR0dHg8/lSNefi4qK1hBSsw9NTCCGYP3++2uHkb968AY/Hw4MHDzB+/HhpBFRZQJLJXj6cnCncv38fXC4XHz9+xMyZMymdmysJXYaTM4GSSn9t2LAB06ZNo/2FQ994/fo1fH19NV7OI1FzHh4e0tJfdKs5RbAOT0/Zu3cvBgwYoFQ4uWReR1bN1a9fHxYWFti+fbveqzlZ3r9/DycnJ4SEhOg89ZIs6enp8PX1RXBwMH799VcsX76clodrcedSF+Hk2qSkcy2v5uSTxV+4cAFxcXHYsGGDFiylDrqv75ycHCxcuBCurq5qp0ajo5Azm1qsnHHnzh3cvXsXPj4+Sm3/5s0bCAQCPHnypMypOVkk4eRHjhzRqNI9lUjUXHx8POWRlqrg4uKCtm3baiWcnAlI1JyLiwuEQiFMTEwUFnL++vUrtmzZoleBTdpixYoVWLZsmcqBO7oo5KwsrMPTM1JSUmBra4vg4OASL6C8vDyEhYXB29sbdevWhZmZGXbu3MmIi44u1q1bh3nz5qFly5Y6S5gNaE/NKcuzZ89w7NgxWsPJmYK8mnN0dCw2+4wky8y+ffvY6hByBAUFoWrVqhg1apTS+zCl9FdJsA5PjyCEYMGCBdi2bVux0ZOSubmHDx9K1ZzkZi7Lzu706dNITU3F1KlTAejmWGXVnDbn5mQRi8WF/paEk/v4+JTZeTuJmnN1dYVIJCo0N1cSjo6OGDlyJDp27KglS6mFrmtc4riUUb26KP2lSdusw9Mjjhw5gh49eqBXr16FPpeoOS8vL/z444+wtLQsNDeXn5+vC3O1Rnx8PHbt2qWT6hDyas7Gxga//PKL1u2QIP8wWLZsGdasWYMGDRroyCL6+Pr1K1xdXXHu3DlpFhRlo3KvX7+O58+fw8PDg2Yr9Yu8vDxYW1vD2dm5xKLRuiz9pQmsw9MTHj16hIsXLyIgIED6WVRUFHg8Hh49eoQJEybA09OzTM7NlYRIJIKlpSUOHTpUar03KmGCmisNLy8vNGrUCIMGDdK1KZQhFotx4cIFuLi4QCQSwcTEBCtWrFApkCExMRHr1q1DWFhYmR71UAdbW1vMnz8fxsbGRb5jeukvZWAdnh4gG04uFAoRGhoKb29vqZrbsWOHXl10VLJp0yZMnTpVK3Nk6enp8PHxQUhICDp27KhzNacIyYM/KioKfn5+0iUa+s6XL1/g5uaGc+fO4a+//ioSaansKIZkOc+uXbvKfBFoVTl27Bjy8/MxYcKEQp/rW7L4kuAQJsVu00xaWhqMjIyQmpqqNxc7IQQmJiYYPnw4Hj58KFVzM2fOVFrNSR4GdFRd1iUXLlyAl5cXXFxcinxH5THfu3cPXC4Xnz59wsyZMzFhwgTGqTmgYL7up59+AiEE3bt3h6enp8rlgpiEIjU3dOhQhXNzyp7vffv2wdDQEIsXL6bFZm1C5TUeFxcHMzMzHDt2DJUrV1ZY+qtPnz6MeLFOSkpC3bp11XqOl60nYBkjNzcXS5cuxZ07d1CpUiVYWFiUazUny9evX7F582bawsnT0tLg6+srVXP//PMP49RcceTk5GDRokV66+xk1dyAAQOwa9cuSipd3L17F7du3WKrQ8ghKRrt5OSEDx8+SBNS6LuaUwSr8BiIZG7u2rVryMjIwOXLlzWaEC5rCk8sFmPixInYuHEjOnXqpHAbdY6ZECKdm5OouYkTJzJmTV9pZGZmon79+hCJREhKStKrUHuxWIz//e9/cHFxgVgsxrx58zBkyBClExWXdr5TU1MxYcIEBAcH60VwhTJQdV+vXr0aOTk5iI6OlqYX7N27N2NfrFmFVwbIzc2Vrptr0KABZs+ejfv37yM0NFSnmQmYiCScvDhnB6h2zGlpafDx8UFoaCg6deqkV2pOlujoaAiFQr1ydF++fIGrqyvOnz+PAQMGYPfu3WqpuZLOt2Q5z9atW8uMswM0v6/fvHkDOzs7XL9+Hba2ttiwYYNeqDk204oe8/r1a/B4PDx58gQTJkyAl5cXatWqBQsLizIbTq4J169fx7Nnz+Dp6alRO4QQ6dzc58+f8ffffyMiIkJv1Jw8eXl5WLZsGapWrcrYN3MJitTcv//+S1u9OWdnZ3Tp0gV9+vShpX19Qja9YLVq1fDu3Tu8evVKr16SNIF1eDogNzcXoaGh8PHxQcOGDWFhYQFHR0fpg6oshpNTARXh5PJq7t9//0WbNm0otlT72NrawszMDPfv39e1KcXy+fNnuLm5aazmVOHx48c4e/YsgoKCaO2H6ciX/nJxccG8efPg7u5ebpwdwDo8rVKcmpPfhupwcqa/8SuDJJx8586dSo3byx6zRM3xeDx8/vwZM2fO1Gs1J48knHzs2LGwtrbWtTmF0JaaU3SNZ2RkwMbGBn5+fmUyy0xp97V86S9LS0tp6a9NmzZh4sSJaN++vZaspQ420wqDkag5b29vNGrUCJaWloXUnCyS7ORubm5lJsCEKvbv34/ff/8d3bt3V3qftLQ0BAQESNXcihUryoSakyU2NhYHDhzA8ePHGZVR5/Pnz9K5uYEDB2LPnj1o1KiR1vonhGDx4sVYv3496tevr7V+mYCi9IKyS5guX76Md+/eYe3atTq0UjewT1WaeP36NbhcLp4+fYqJEyfC29u7VGWyYsUKLF++XG/Dyeni7t27uHHjBvz9/UvdVqLmjh49iq9fv2LWrFllSs3JIhQKYWVlJa0OoWuHJxaLcf78eem6yHnz5mHVqlU6UVfu7u5o0aIF/vzzT633rQtkk8WXVPrr27dv2Lhxo0ZFo/UZ1uFRSG5uLkJCQuDj4yNVc8pWKAgKCkK1atUwcuRILViqP6SmpmLlypWlVodIS0uDt7c3QkND0aVLF/zzzz9o06ZNmVbK9vb2mDt3Llq1aiX9TBcRuRI197///Q8DBw7E3r17tarm5ImMjERISAhCQ0N1ZoO2ePPmDVxdXYtVc7JIqkPs2bOn3FZ1L7tPAy3y6tUr8Hg8ldScLO/evYNAIGBrcslBCIG1tTW2bt2KOnXqKPz+7t274PF4+PLlC/7++29ppghdqx26OXPmDBITEzF9+vRCn2vrrZ1Jak6WrKwsLFmyBJ6enrRFfeoa2WTx9erVg5WVlVKFnHfv3o2hQ4eic+fOWrKUebAOT00Uqbldu3ap3I5sdvKKFSvSYKn+Igkn79u3b6HPU1NTpZGWXbp0KTORlsry6dMnODo66qQ6BNPUnDw2NjZYtWoVo2yiCsnc3KNHjzB+/Hi4urrCyMhIqVGMmzdv4tGjR/Dy8tKCpcyFdXgqIq/mfHx8ULNmTbXbKyk7eXlGPpy8JDVXnpBUhzh48CCqVatW5Hs6hjTl1ZypqSkj1Jw8fn5+qFu3LoYMGaJrUyijpNJfyo5iJCUlYc2aNWx1CLAOTylk1Vzjxo3VVnPyFJedvLwjG04uqVAgUXMrV65E69atdW2iztiyZQsmTZpUbDg5lQ+0z58/w8XFBRcuXMCgQYMYp+ZkiYqKgre3t05ULx1QVfpLspzH0dGx3JUOUwTr8Erg5cuX4PF4eP78OSVqTpa4uDgcPHhQKzeoPqUWk4STT548Gba2ttJIS1XVnD4ds7JcunQJ0dHRWLduXbHbaOrwxGIxzp07B1dXV3A4HMybNw+rV69mnJqTJScnB4sXLwaXy9XrICX59IKlJYtX5ho/ePAg+vXrh549e1Jtrs5gU4tRSE5ODkJCQuDr6ytVc6qs/VIG2ezk5W1IriRSU1OxaNEi3Lx5Ez/++CNWrVpVrtWcLJJw8oiICFqGpT59+gRXV1epmtu3bx8aNmxIeT90sHLlSixcuBBNmzbVtSlqQVch53v37uHq1auFikaXd1iH9x1ZNTdp0iRK1Zw89vb2mDNnTqFw8vIKIQR37twBj8fDu3fvkJaWhidPniicnyqviMViWFpaYu/evZSGk+ujmpMnJCQEFStWxOjRo3VtikqoquZURbKcJygoqNzP28lSrh2eRM35+PigSZMmsLCwoFzNyXP27FmF4eR0wsQLPjU1Fd7e3ggLC0PXrl2xZMkS2NjY4NixY5Q4OyYes7rs2rULw4YNUyqcXJnhHn1Wc7JER0eDy+XSpnrpQF7NKUovqCwlDXUuXLgQmzZtUricR99hU4upyOvXr+Hj44PIyEhMmjQJvr6+tKk5WSTh5OV1vZ1EzXG5XCQkJGDWrFk4fvw4KlWqhPnz55fZcHJNuHHjBh4/fqxxOLlEzbm4uMDAwACmpqZ6p+ZkkSznOXLkCCpVqsTodZeyak6SLJ7OQs48Hg+//vorfvvtN1ra12fKpcNzcnLCokWL0K1bN631KRKJYGVlhQMHDpS74brU1FR4eXkhLCwM3bp1g62tbaHhXF9f3zIXTk4FSUlJsLOzUymcXF7hxcfHw9XVFRcvXsTgwYOxf/9+vVRz8tjZ2cHCwgI///yzrk0pFmWSxVPNkydPcPLkSYSEhNDaj75SLh3evn37tF7xfOvWrXqbnVwdCCG4ffs2eDyeVM2dOHEClSpVKrRdVFQUPD09y63qLQ51w8k5HA4IITh37hx8fX2las7W1lZv1Zw8J06cQE5ODiZNmqRrU4pQWukvOsnIyMCyZcvKbHUIKiiXDk/blKfs5CkpKfD29kZ4eLhCNSdLbm4uFi5cCIFAoNfh5HSgTjj5p0+fkJOTg/z8fDx58qTMqDlZPnz4gH379jFuvZ0u1Jw8S5Yswbp16/Djjz9qtV99gn3K0Ex5yE6uSM1J5uZKYuXKlVi8eLHehpPThSrh5CKRSBppKRaLYWhoiEqVKuGff/4pc4U9Jct5Dh8+jCpVqujanCKlv7Sp5uRxd3dHs2bNMGDAAK33rU+wDo9Gynp2cnk1t2bNGrRs2VKpfUNCQlChQgWMGTOGZiv1C2XDyWXn5oYMGYIDBw6gRo0aZbq0lIODA/7++2+d501Vp/QXnbx8+RJBQUGUFo1mIpLSXwcOHFC7Ddbh0UhZzE5OCMGtW7fA4/GQlJSktJqTJTo6Gs7OzowbltI1pYWTi0QinD17Fq6urqhQoUKRubnMzExtm6w1zp8/jy9fvmDTpk066V+T0l90kp2djUWLFsHDw6PMVoeQLf3VuXNnLF68WO2oZdbh0QSTspNTkWYrJSUFXl5eCA8PR48ePWBnZ6e0mpNFEk5+9OhRlZykquhjarHiwsnj4+Ph4uKCS5cuYciQITh48CAaNGigsA1dP4Dp4PPnz9i+fXuJgU10nW+mqTlZCCFYsWIF/v33XzRu3FjX5lBKScniExMT1W6XdXg0kJycDDs7O4SGhur1A0iRmlMUaakKdnZ2MDc3Z3Q4uS6QDydXpObWrFlT7qLvJMt59u/fr7XlPFSV/qKbgIAAGBkZYdiwYbo2hTJkS3917tyZ8tJfrMOjGEk4+Y4dOxiTnVxVp0uVmpPnxIkTyM7OxuTJkzVuqzT06UVDNpxcUqFAGTWnCH1UtiWxfft2jBs3Dh06dChxOyrOt6T0V0LiLSxcXAP+wTVQqUJdGHCUuI9zo4BEFyAvBqhkDNQ1BSrTlwf27du38PLyKhPr7VQt/cVmWmEQhw4dQt++ffUuO7m8mps9e7bGak4WpoaTM4HFixdj6NChWLRoESpUqAAzM7NyqebkuXr1Kl6/fo01a9bQ1od86a+VqxuiSfObADgACETgQEQcUQECGHJMFDeS6ArEmUv3ATjAV0egqQCoW8w+GtosmRbQ56LRuijkzDo8Crl//z6uXr0Kf39/XZuiNCkpKdKF3z169MDatWvRokULSvtgWjg5U4iPj8fixYvx4MEDtG3bVmU1p4iyovASEhKwYcMG2oqWvnr1ClwuF8+ePZOW/qpe4zOEpC0AcZHt84kZDNAfHI7cmtLcqO/Orug+iDMDavQHKn/fJzUKeOUCZMQANYyBX0wBI9VV4KpVq7Bo0SI0a9ZM5X11jWyy+K9fv2q9kDPr8CgiLS0N//77r15kJyeE4ObNm+DxeEhJSaFkbq4kHBwcMHPmTJ2HkzMBkUiEM2fOwM3NDVlZWUhISMDr168pe1Nn+rWnDGKxGPPnz8fu3bspzXFbWumvfPFWFKg0RXAgIgJU4Gwr/HGiS4n7IFEANN4GvHIFrsqpwCeOwB8CoI2J0scgeQEYO3Yso/OHyiObLL5Lly46K/3FOjwK0Jfs5MnJyfDy8kJERAR69uyJdevWUa7m5Dl//jw+f/6ss3BypvDx40e4uLjg8uXLGDp0KHbu3AkzMzNpeRuW/9i7dy8GDhyILl26qLxvDqKQABfkIQaVYIx6MEXMSxF4PB6ePXtWYukvghgUOCNFkO/fy5FX8j7IiylQdlfNAaJABV4xAxr0B4xKLxX2/v17HDlyRG+mBeTVnDqFnKlGrxzelStXsHPnTty/fx+fPn1CaGgoxo8fr2uzwOfz0aFDB0ZmJyeE4MaNGxAIBEhNTcXs2bNx8uRJrTxkP3/+jG3btpXbPJmyaq5ixYowNTWFnZ0dDAwMYG1tjRUrVlAeTq7vQ5q3b9/G/fv34e3trfK+iRw3xMEKAAcgBIQA8diOK7f+xMyZu0st/cWBMUpSawXfy1Gp5H1QybhgGLOkbV4JgF7bivm+AKFQiPnz58PJyYnW5TxUIF/6i0mFnPXK4WVmZqJz586YN28eYxLHPn36FCdPnkRwcLCuTSmErJrr3r077OzstDqkKFsdoqyluCoNeTV36NChQvkN/f39YWRkhOHDh1Petz4PaSYnJ8PW1hYhISEqH0cuohBnYAXpXBoH4HAADgH+MrmKDig90tKAYwoRcSzmWwJDjlnRj+uaFgSoFLMP6poBL9ehRBWYEVOqbevWrcO8efMoiZamA1k19+3bN63PzSmLXjm8ESNGYMSIEbo2Q0pmZiaWLVsmzUqvayRqjsfjFVJzungIbt++HWPHji01nLysIBKJcPr0abi5uaFSpUowMzOTqjlZ3r59Czc3t3KreouDEAJra2ts374dtWvXVmnfnJwcXH2zEj+0IyiSbIRT8D8JEKAJSlZRBpzWqAAB8okZCs21gaACR1A0YAUoWHrQVFAQoCK3D5oKCgJWahijRIVXw7hEu06fPo20tDRMnTq1xO10AZPVnCL0yuGpSm5uLnJzc6V/p6WlASgYHhAKhaU6AtnhIUXbLlq0CLa2tvjhhx8gFAqL3U6VNhVtW9p2SUlJ8Pb2xokTJ9CzZ0/Y2dkVWtgtsU2V/tWxU7LttWvX8OLFC6xcubLIxLqyx6RJ/0DhY6aqTUVI1Ny1a9cwdOhQ7N+/X6rmxGIxxOL/5m1ycnIwf/58HD16FBwOp8SgA3XOU35+vnTtp0gkKva3L61N2W3pPk8SDh8+jO7du6Nbt26Fzl1Jbb58+RJ8Ph8vXrzA8oOJMDSQOJwiHSOHREMoUuYenQUO6Q3CcQXwHhyOMThkHghaIR9FzxchBKj1N9CqNwxT3ADhe6Bic4h/mFfg7PLzgZZzYPikQAXK9kwAgIhBHj4BYldB3M8E+LF1od/p06dP2LVrF0JDQ4ucT8nvRAjR2nmSfH/nzh3w+XwkJCRg5syZCAsLkw61Krquqbz2FN3bylKmHd62bdvg4OBAS9uenp5o2rQp/vrrL53Mm0jUnIuLC1JSUvD3338jIiJC5+P7CQkJcHBwUGtYSl+QzM15eHigYsWKmDdvHtasWVNqLsM1a9bA2tpaL8PJ6eTBgwe4cuUK/Pz8St1WEmnp7++Pn376CWZmZujWrRs+Yg0S8KiYvTiohOZK28NBK3DIlu//X8lruHIriBtuUfydUWuI+nFheMMSRKL+CAqCWGIATsJpgHMGhmd3QTybC9JnDoCC68za2hr79u1D1apVlbafLlJSUuDj44OIiAh07doVK1eulJb+0pd7vUw7PFtbW9jY2Ej/TktLQ9OmTVGxYkWNgjZevnyJ4OBghIeHaz1ha3JyMjw9PXHs2DH06tULGzZsKDVNl8Qh011zTiwWY+HChdizZw9++OEHWvsqDTqO+cOHD3BxccGVK1cwbNgwODk5KV17LCwsDIaGhpg4cSJl9shToUIF6SiGoaGhXtQYTEtLw+rVqxEYGFjiPfnixQvweDxERkZi0qRJ8PPzKxRpWU84DwnYo3hnDsGPHAtUNNBhNGx7M+CnPwsCVBKeAvdOAF8B5BJIHSAAQ09LGP7yJ/BjK2zZsgXTp0/Hr7/+qrBJyTVOZwCaotJfJ0+e1OmLdXR0tNr7Mv+O0IDKlStTPmmqi+zk8nNzc+bMUSnSUltvX5Jw8q5du2qlv5Kg6pgVzc2tXbtWpTlbbYaT61OUJiEEKzbNwQL3xnhQdxFqwhhtYYraKJgDysnJQXBwMHx9fdGkSRNYWlqiW7duCtuqwmmDpmIu4gwtIT+XZgwBqqD0sH/aMWpVEI0ZYgt8PA2IRUW34XCAawJcqD0EcXFx2LBhQ7HN0Xlfq1LIWZtkZ2dj1apVau9fph0eHdjY2NASTq6I5ORkeHh44NixY+jduzfs7e0Zm3T59u3buHv3Lnx9fXVtCiV8+PABAoEAV65cwfDhw+Hk5IT69eur3I62w8n1yeHxrpiiy44IJBgYIOG7g3oER7SJ34TjuxIKqTll6knWJXNhhD+RAIHMOjwzZjg7WRJigOLOEyHI+fgSWw7f0Xpgk7qFnLXJihUrsGDBAly5ckWt/fXK4WVkZODNmzfSv6Ojo/Ho0SPUqVNHK/MidIaTSyCE4Pr16+Dz+UhLS8Ps2bNx6tQpRi9OTk5OxurVq/W+OoRIJMKpU6fg5uaGKlWqwMzMDOvXr9fomLQdTq4vv//d1yeQ/7sbOAYFGSslEAK8bLgWk81C0a9DMUOUJVAFrUqNxtQ59YwLlJyi+BoOByduPce+fcFaW84jmyy+e/fuKhVy1iaBgYGoXr06hgwZonYbeuXw7t27V6iEvWR+bu7cuXBzc6O1b7rDyZOSkuDp6Ynjx48zXs3Jokk4OVOQqLmrV69i+PDhOHLkiFpqTh4mh5PrkszMTHjdW4h2rQ0LOTvg+9o5jgEMOtwCME43BtLNb6bAacVr94hYjPw+c9GxY0daTZBNFp+YmEh5sniqeffuHQQCAY4dO4b09HS129Erh6eriEhJdnIej0ep0lKk5rSVBYUqnJyc0LNnT/Tu3VvXpqgEHWpOlvj4eOzevVsnw1JMZ9GiReiwrBpEYhEMFE6DE6QrSuNVVmjQGpgrANzNvis9AnA4IISAn9cbFovoqw5BV+kvOpEUjXZ2dtb42ahXDk9XrFq1CgsXLkTz5sqHNpeEvJrbsGEDjI2NKWlbmzx8+BAXLlxAYGCgrk1Rmri4OLi4uFCu5mQRiUSwtLTEwYMHtR5OzuQhzRcvXmD5okWIiolBn6W/gBi8LqLwCuCgpqI0XmWF91HA/VeA0QigYiJQvy6yf2wFC/dbcAo6Tfk5pKOQszZZvXo15s+fT8kzknV4pRAWFgYAGDdOs+EVQgiuXbsGPp+P9PR0lSMtmUZ6ejr++ecfBAQEMCLLTEnk5+fj1KlTcHd3R5UqVWBubk6pmpNn06ZNmDZtGtq2bUtL+/pEdnY2goODC5YRpKcj8/VrvIqLQ0aFaPihuN+HoB0UpPEqC4S5AhvNiyg7l/rdYLPdGbVq1aKsK31Uc/JEREQgPz8fEyZMoKQ91uGVwPv37+Hk5KRROHlSUhI8PDxw/Phx9O3bFw4ODnqp5mSRVIdwcHBAvXr1dG1OscTFxcHd3R3Xrl3DiBEjaFFz8ly4cKHUcPLyQGRkJHg8Hl6+fInJEybAtUULzDh4EH4CASpUqIDaaI2/IMAlFE3J9RcEMGJaZCUVvI8qcHbiolUTrL/eh0E9zZ0d3YWctUlsbCwOHjyI48ePU9Ym6/CKQRJOfuTIEZXX8ilSc7qMtKR6XsfFxQW//PILfv/9d0rbpQKJmnN1dUXVqlVhYWEBe3t7rQz1ff36FVu2bNFpnkxdDmlK1Jyvry+aN28OCwsLdK1XD5gxAwuvX4dNjRr4adYs6fZtYYJG6I8XECAdMagJY7SDmVrOTh/mLhHuUqDs5OAAgIEBECYAligfYSp7zNoo5KxNhEIhrKysFD5/NTnXrMMrBnXCycuimpPn2bNniIiIQEhIiK5NKURcXBwEAoFUzR0+fBj16tXT2kuGWCyGlZUV9u3bVyarQ3xBFK7CBQmIQT0Y43eYosH3BeKRkZHgcrl49eoVJk+eDH9//4J1cydOAIMHIzApCdUBjJw9G5BTGkZohT5MX0ZAFfExxa6/4xBS8L0KSNScq6urVgo5axN7e3vMnTuX8sXurMNTwOnTp5GamqpUOLm8mps7dy5Onz6tF2mdVCUzMxNLly6Fj4+P1lOqKUKi5tzc3FCtWjWYmZlJ1ZwmCWbVwdHRESNHjqQ9nFwXXIUr3GAODjggIOCAg1PEEb/cMMPlrR/RvHlzWFpa/lewVSgEVqwAdu/GOwACAMcAYPZsnR0DI2hsrFDhASj4vLGxUs1ISn9J1s1po5CzNjlz5gwSExMxffp0ytsue09lDYmPj8euXbtKnbdLTEyEh4cHTpw4gb59+2Ljxo2URXFSDVXDXMuWLcOaNWvQoEEDStpTl7i4OPD5fFy/fh0jRoyAs7NzkblEbQ7tXb9+Hc+fP4eHh4fW+iwOsYL5IU34gii4wRwEYuk66e/ZH/GyLx+HAh7i5+qd/9vh/Xtg2jTg9m3kAbAG4AygYsuWQJ8+lNomC5OjU6WMMwXciqmdRwgwvvhAHUIIbt68CR6Ph+TkZMyePRvHjh1DxYoVy9TL9adPn+Do6Fji81eTc112fikKkISTHzp0SGE4OSEEV69eBZ/PR2ZmJubMmVNm1Zw8Xl5eaNSoEQYNGqST/vPz83Hy5Em4u7ujevXqMDMzw4YNG3T+oEtMTMS6desQFhamc1sA6h/8V+ECDuGAyDXL4QAGHAPcr+6Hn/Hd4YWHAyYmQEoKAGA1gPlAwQKDWbOKVzflheatAXsByAYziAmBgQGn4HwRAtgLgGZFh+9kCzn37NmzkJorqbyUPiK7nKdatWq09FH2n9QqsGnTJkydOrVIOLmsmuvXrx82bdrEWDVHB69fv4afn590iYY2iY2NhUAgwPXr1zFy5EiFak5XEEIwf/587Nq1i9Jwcqbw/PlznM0JgaiLCBwFI9gEBAmIAfLygJUrgf37pd9FAMgHIA0mlwlWKc9kDJoM673OcB7eC9VSvhYMY443K+TsiivkrK9LmJRly5YtmDRpEtq3b09bH6zD+86FCxcQGxsrDScvz2pOlpycHCxcuBBubm5aO3amqjl59u/fjz/++KPYDP66QNNoxezsbAQGBsLf3x/GxsbovP43PDR8C7GCBeIccFAPxkB0NNCwITBzJnDuHGK/fcNBANJg8j59AAZk2tc1hBAsXrwYFht3oNoffxT5Xr70l76kF6SCS5cuITo6GuvWraO1n/L19C6Gr1+/YvPmzYiIiCj3ak6eFStWYPny5fjpp59o74vJak6eu3fv4tatW4yrDqHuS8Hz58/B5XLx+vVrTJkyBQEBAahevTq+IAoP4K5wHwKC32EG/NIKWL0aePsWwmPHYAXgCABpMHl5D1b5jpubG1q2bIk/ZJydRM3x+XykpKSUGzUny7dv37Bx40ZERETQ/lJb7h2eWCyGpaUlZs2aBWtra2RlZZXpSEtVCAoKQrVq1TBy5Eja+pBXc+bm5oxUc7KkpqZi1apVCA4OZrSdpSFRc35+fvj5559haWmJzp07F9qmAVpjHgRwhVmhKE0CgnkQoIFkzVxuLjBtGuzT0zEXQKtffwWePQMqVADKa/LscxeA9duB+C/I+qEm3lUBNly/DKComlu/fn25UXOySJ6/e/fuVaoElKaU6yd6QkIC5s6di3fv3uH9+/fYsmWLVsoM6QOS7OR0LaKOjY0Fn8/HjRs3MGrUKHC5XNStW5eWvqiEEIIFCxZg69atOq/qrghlhjSfPXsGLpeLqKgoTJ06VVp2pTj6wwSt0R9XIZBZh2f2n7MDgNWrceb+fSQCmN6mDXD9OvDnn0CzZgBDVTqtmC4CXIMAFES0Vo39go0AvoyfAdt61ZGSkqL36QWpYNeuXRg2bFiRFy26KJcO79q1a/D19UVcXBwA4MmTJ2X6olN1XofK7OSy5Ofn48SJE/Dw8JCqOQcHB1pUEl2ZN5ydndGlSxf0oTHEXhOKy2uanZ2NgIAA+Pv7F6vmSqIBWmFycQvEIyLwad8+OAI4VqkS4O8P1KoFODgUBLRoAUZlWjl34buzK7iuJVc3AUGD41ew1XMvGs2aoXE3jDpmNbhx4wYeP34MLy8vlfZjM62oyJUrV6RzU2FhYWXa2amDra0tZdnJgYKcpAKBQO/UnDyPHz/G2bNnERQUpGtTlEai5t68eYMpU6aUquZUJjYWorlzYQngIIBq+/YBkgXoY8YULEIvJ4jFBIlZQlRfvQVV8Z+jk8D5niu00WFXgAKHp88kJSXBzs5O68t5yqXDs7W1hbm5eZkNJ9eEY8eOUZKdXKLm3N3dUaNGDVrVnDbIyMiAjY0N/Pz8GFsdIpbzBrXWZ8OwqRgLXk9G/OEs/FKlIywsLOgZMhIKgRkzsCUlBZMAtJ88GZg//7/vOZwiqcT0lfScfFyPTsOX9Dx8Sc/D1wzh9/8vxJeMgs++ZQghzk5DzPPXKHFiJP6LtsxmJJLlPI6OjjAyMtJq3+XS4R05coRx4eR0oqyTiY2NxYEDBzTKTv7+/Xvw+XzcvHkTo0aNAo/H04mao9KxSsLJ169fT3u1BXUJhSvWVzVHjcVigAM84JwFhwcs5MxDZ9A0P7J+PS7duIFoAOuMjQEeT2eLy+l+kapeyRAXopKx8+KHol8SAsQ/BZ6dAPKy8LFqTTTLTSq+scbUZCrS15fHgwcPol+/fujZs6da+7OZVlTk7t27ejUspQ1Kyk5eGvn5+Th+/Dg8PDxQs2ZNmJubY+PGjXp7Q8rj7u6OFi1a4M8//9S1KUXIysoC9/RB8MevBgwAzvc7WpIKbD3M0A390YzqcjtnzuDb9u3YCCCiQgVwAgKA2rWp7YNBGBhw4Di2JepVr4hVx6MLPsxJA16cBaJvAg3bAX1MULXeT8hu/hVYtFAa0fof3+eeNtNX0Zzp3Lt3D1evXkVAQIBO+i+XDm/Pnj1l5mFMFepkJ5dVc6NHj9aZmqOTyMhIhISEIDQ0VNemFOLp06fgcrl4+/YtGm7nwJBjCFExi8ODIcByKisSxMdDPGsWLAHsBVDD0RFQ821dX3jxJRO8m5/gducz8PGJVM2h3VBg3A7AsAKa/1AZoaYdEH3nHO782gy9n8VC6uQkmE0BBv2li0PQOampqVi5ciWCgoLUev6KRCKcOnUKPB5PbRvKpcNjYji5LlElO7lQKJRGWpZFNSdLVlYWlixZAk9PT0ZUh8jKykJAQAACAgLQsmVLWFhYoFOnTvgXM0DkH6zfISCIRwx1RohEwN9/Y1dCAoYB6Dx6NLBsGXXtM4gcoRjBT77B+cYnXI2MAyLPFKi5Rh2APiaAUSPptoPb1Ibv7PZI//YBXC4XEfevAVdvAGu3FszZNW5QoOzKqbOTFI3etGkT6tSpo9K+8qW/du3apfZyqXLp8Fj+Q5ns5AAQExMDgUAgVXN8Pl/lC1ffsLGxwapVq9CoUaPSN6YRWTU3depUaUIACY1hLDd09h8ccNC4IH0zNWzejBuXLuExAK+ffgLc3MpcUugXXzLBvfEJ7nc/I/nNw0JqrvKUXZjctSG873+Vbr9yYFNsGfkzxCIhZllb48iRIwU16Qb9VW4dnDw8Hg+//vorfvvtN6W2l5T+cnd3R9WqVQuV/kpKKmF+tBRYh1eOKS07ubyas7CwKLNqTh5fX1/UrVsXQ4YM0Un/EjXn7++PVq1awdLSsthaexNhClc4FoyeyZ0aAoJJKL7sjEpcvIikDRtgByDMwAAcPz+gjAxh5wjFCHr8DdybitVc+zYtYdWvEWZ1b4B8MYH3/a+oVskArtN/wdSuPwIA/l1tBwsLi3KZMaUknjx5glOnTiE4OLjUbeXV3NGjRylNL8g6vHJMcdnJY2JiwOfzcfv27XKj5mSJioqCp6cnbVlmSuLp06dwdnbGu3fvMG3aNAQHB5daKqU5WmMjBFgPM4jyC+rhVTA0BOEQbISAmoCVr19BZs7EfACOAIw2bwb699e8XR0T+fn73Nzdz0iRVXPth6Hy1F2Y1rURLPs2Qr+fa0lf9J5/ykTLelUQOq8DOjYuSId14sQJ5OTkYNKkSbo8HMaRkZGB5cuXw9fXt9jlPPJqztzcXKrmqIZD9H25vgqkpaXByMgIqamp5Wr9naRulmxu0EuXLsHd3R0uLi7SCuGSSEsjIyOYm5vjt99+01s1p+iYlSE3NxdjxoyBQCBA06ZN6TCtCFlZWfD390dAQABat24NCwsLtSqnv8x6gqFHe6FCMzHmj12C6ZXmU+PsxGJgxAgcOHsWYgDLhg4FTp0CGLQeUZXznZ0nQvCTBDjfiMe1yLj/Ii0bdQB+HYX2rVvAql8jzO7RAD9Uk0tKEfURGUdOolLcN1Rq1RAwHYYPVQnmzZuHY8eOoUqVKnQcnkLUvca1iZmZGWbPno2//vqryHcSNScp5Dxnzhyl1FxSUhLq1q2r1nOcdXjlAOH3bBeSjDLfvn3DtGnTEBERgYSEhEJqbvbs2WVCzckfs7IsXboUgwcPxpgxY+gwqxBPnjwBl8tFdHQ0pk6diilTpmhU+DIzMxNNmjQBAHz48IG6jCrbt+OerS12AAho0ACcJ0+AH3+kpm2KUOZ8R37OBPdmwdxcStQD4PkJQJhTMDfXph+mdW0Eq36N0Ne4luIXPdezgPnegjlLQgAOB4QQ7PsVGBW4H23atKHr8BSi7jWuLdzd3RETEwN7e3vpZ7Jqrlq1ajAzM8Mff/yh0ot1YmIi6tWrp9ZznLmvBiy0IBaLYW5uLnVuEjW3adMmvVVzVBEaGoqKFSvS6uwyMzOlkZatW7eGlZWVWmpOa1y/jlQ7O6wEEASA4+vLOGdXEtl5IgQ9TgD3ppyaa/wr0NcUHdq0gFXfxpjV48eiak6WqI8Fzk5M8N9Sg4J/lz0FOAb0Z/rXJ16+fImgoCBp0Wj50l9Uz80pC+vwyhExMTEwNTVFfHw8Bg4cCIFAUCbUHBXExMTA2dmZtnk7iZpTZW5O5yQmgkyfjoViMTYBqGNvDwwYoGurlKJENTd1F6Z3K5ibK1bNyeNy5ns0auEBMQ5QMLQrOA1sM6XjUPSO7OxsLFq0CC4uLtL0gkwp5Mw6vDKOUChEWFgYvL29IRQKUaFCBURGRjI2HyRVqHJTCYVCWMuGk1NEZmYm/P39ERgYiDZt2mD+/Pn49ddfKWtfEZTNUBACzJsH3ocP+BXAb3/9BdBcjVoTOBwOsvNE8Hv0RXM1p4iYLwW/iSLI9++1DFNHZCwtLdGgQQOYmprSUsiZTS3GUoTo6Gjw+XzcuXMHI0eOxI4dOzB//nyEhYWVeWenKnZ2djA3N6csnPzx48fSubnp06cXUnNReANXeCIGsTBGM8zDbLSmOu0XFezfjyfHjuEkgJC6dQFvb4ABi+8V8fxTJtzvfITfw6+Ie36/INIyPxdoN0w9NacI4wYKFR6AAplnTE1+TH1FUsh5y5YtyMzMxOHDh1Wem9MGrMMrQwiFQhw7dgyenp6oXbs2zM3NsXnzZuTn52PmzJk6yU7OdE6ePIns7GyNw8nl1Zy1tXURNecKT1hiUaHK4TuxDzwchglmadS/BEoU3t27yPj3XywD4AfAwMsLaNxY83YpRDI353wzHtcj41D59Rnkv7sFNOwI9DPHr7+0gGWfRuqpOUWYDgMcAxV/RwhgNlzzPvQQ2ULOvXv3Rq1atXDt2jXGBtKwDq8MIKvmxo4dCxcXl0Lp0w4dOoQ+ffqonZ28rPLhwwfs27dPo3k7iZqLiYnBtGnTEBISgqpVqxbZLgpvYIlFEENc5DsLLER/9EUrtFTbDgkav1GnpgLTpmFJfj7WAfhx1SpgOHMe5s8//Tc3l/rmPzVn2HEYjGbuwsiOBWquT3MN1JwiWv8ECJaDmO2FmBAYcAy+Cz4CCJYDrZj1QkAnigo5r1mzBmPHjoVAIGCsswNYh6e3SNSch4cHfvjhB1hYWGDz5s1FbvJ79+7h+vXr8PX11ZGlzCQ/Px9WVlY4dOiQymun5NXcggUL0KFDhxL3cYVniem/XOCBrXBQyQ7KIQQwN4d7dDSaARjQty+waZNubUKBmgv8ngXlemTs97m5W0Dj/9Tcwr4NMKVLfdStSd86uITR3bC8Vx74/aagcnxywTCm2fBy4+xKKuS8bNkyLFq0CM2alVgJUOewDk/PiI6OBo/Hw927dzF27Fi4uroWmwxbkp3cz8+PcWPpusbBwQF///23SmunHj9+DGdnZ7x//x7Tp08vVs0pIgaxJSZ4jkGs0naUhEZDms7OeBkUhEAA4bVrA76+gA7f1otTc2g/HFWm7sL07v+pOZGoaKUIKhGLxZg/fz7WHtmNypKK7uUARWpOvpCzpGr52LFjdWipcrAOTw8QCoWIiIiAp6enVM1t2bKlRCemSXbyss758+fx5csXbFJCvWRkZEjVXNu2bbFw4cJS1ZwijNGsRIVnXHKNbKVR+8Xm8WNkL12KRQA8ABi6uQHNm1NikyoUUXORZ4CY24XUnFXfRpjVowFqV9Xe42vv3r0YOHAgupQTZ1eSmpPfzsnJSaOi0dqEdXgM5t27d+Dz+UqpOXlks5NLUhCxAJ8/f8b27dtLnbd79OgRuFyuVM2FhoYqreYUMQ+zsRP7FH5HQGCKOWq3rTEZGcDUqbDJy8MKAI2XLgXGjdOqCYXUXNQ94PnJ/9RcrymY3r0RrPo2Ru/mNbU+WnH79m3cv38f3t7eWu1X20jUnLu7u7T0l7yak0W2aDSVy3nohHV4DENWzdWpU0cpNSfPkydPcPLkSYSEhACgcG2WHqHomEUiEaysrLB//36Fi76pUnOKaI1W4OEwLLCwUJQmAQEPhykJWAHUUHiEANbW8H/9GrUBDO/eHdixgxJbSkOi5pxvfMKNF0XVXMdfCnJa/t29dDVH1zWenJwMW1tbhISEMG5agKpjVreQ89q1a2FqaoqWLam5dpVFk+NmHR5DePfuHXg8Hu7du4dx48appOZkycjIwLJly+Dn58eut5Nj+/btGDduXBEn9ujRIzg7OyM2NpYSNVccJpiF/ugLF3hI1+GZYg5lzk4t3N3x1ssL7gDCa9QA/P2BypVp7fLZdzXnUYyam9G9MSz7NtKJmpOFEAJra2ts374dtWvX1pkddJCfny9NFq9OIedTp04hPT0dU6dOpdlSamEdng4RCoUIDw+Hl5eXVM1t3bpVo5t8yZIlWLduHX6UyXfItDdTbSB/zFevXsXr16+xZs0aAAUvBn5+fggKCkK7du2wePHiImWS6KAVWtIajanS229kJHIXLIA1AD6AigIBQNPbelaeCIGPCubmCqm5nzoBv1mgY5uflVZzilDpGo9KBFzuAzEpgHFtwLQ70LqoonFyckKvXr3Qq1cvle3RBurc15JCzrdu3cKoUaPUKv318eNH7N69u9Si0XTBZlrRM96+fQs+ny9Vc25ubpS8Qbq7u6NZs2YYoCf5DrVFQkICNmzYgLCwMOncXGxsLGbMmEGbmmM8WVnAtGlYlZ2NRQCaWVkBNLytF1VzJ4D8PN2pOdcHgHlYQXYUScFcx2uAYDxg0k262cOHD3Hx4kUEBhaz2FyPoLKQs+xyHn28b1iHpyXy8vIQERFBqZqT5eXLlwgMDER4eDgl7ZUVJNUhfvvtN0yZMkWrak4XKK3wli1D2LNn4AAY27EjsHcvZTZI1JzzzU+4GRkLvDgNxNz5ruYspWpuVvcGMNJipCWiEgucnVjBb2QWBvRvDrSqi/T0dPzzzz8IDAzU69EROgo5b9q0CdOmTUPbtm0pslK7sA6PZiRq7v79+5SqOVkk2ck9PDxgyNB8h7rg4cOHWLp0KVJTUzF58mSsWbNGqwU6dYFSD2hfX7zn8XAEwLGqVYGAAICCt/VnnzLhfCMeHnc/I+3N/QI1JxIC7Yahau9pmPF93VyvZjqam3O5j2JWhhR8LrgPsnUIFi5ciI0bNyoVuME0FBVypqr014ULF/Dhwwc4OOg4QYIGsA6PBiRqztPTE/Xq1aNczcljY2ODFStWoDHD8h3qAsncXGBgIGrXro06derg+vXrev2mTilRURBaWGA+ACcAlY4eBTR4W8/KEyHg+9ycIjXX6ZefYdW3YG5Oq2pOETEpCnM/A/he8SAFLi4uaNu2Lfr3769FwzRHXs1RXfrry5cv2LJlC23ls7QF6/Ao5O3bt+DxeHjw4AHGjRsHd3d32qO7/P39Ubt2bQxnUL5DXfDw4UNwuVzExcVhxowZ4PP5mDNnDkJDQ8uVsytxSDM3F5g2DesyMzEPQMu5c4E56q3/exqfIZ2bK6Tm2g9nhppThHHtEhXet+r5OHbsmHQ5D9ORzM15e3vTWshZLBbD0tIS+/btQ/Xq1SltW9uwDk9D8vLypJGWEjW3bds2rdzkb9++hbu7e7mdt0tPT4efnx+Cg4PRvn17LFmyBO3atQMhBNOnT8eWLVvUfuGIwge44CRi8BnGaAhTjERrNKH2AGigxOvu339x+uFDpAGY2rYtcOiQSm0XVnPvCyIt398BfurMPDWnCNPuBQEqCiAEsHnuDecwF8Yv55GouVu3bmHkyJG0F3LesWMHRo8ejY4dO9LWh7Zg4FWpH7x58wZ8Pl+rak6W3NxcWFtbg8/nMzo7OR08ePAAXC4XHz58wIwZMxAWFlZobs7JyQk9evRQO5zcFadgjp2FA/ngBwH+hQlGUHIMWic0FPEHD2I3gIjKlQvW29WoodSuhdXcPeDZSUD8Xc31KVBzVn0boSeT1JwiWtctiMY0CyuobUeINFrTrX8KTNbboEEDZta1k52bk5T+sre3B4fDQYUK9D3Gr127hsjISHh4eNDWhzZhHZ4KyKq5+vXra1XNybNq1Sqls5OXhUwrEjUXFBSEDh06YOnSpWjXrl2R7STh5D4+PmoddxQ+wBw7FZbxMcNO9EdHtGKw0lN4LcbEQDRvHiwBHARQ9cABoFOnEtuRqDnnG/G4JVk3J1Fz/S3R+ZefYdWvMWZ2+5ERak7pc23SrSAaU/DfOryweh8QnRqDeYMG0WqjOsiW/hozZkwhNScUCmm9txMTE7F+/XppcmimwGZaoRlZNTd+/HhpBJSu0Kfs5Jpy//59cLlcfPz4ETNmzEB4eHixkZZUhJO74GTJgXw4iW2wVKttnSAUAtOnY1NqKqYBaDttGmBhUezmT+Mz4HzzEzzvfiqYm5NTczO/z80xXs2VRKu6wLahAIBXr16BZ7OfUdMCxRVy1ubvTQiBlZUVdu3ahVq1ammtX7phHV4xMEnNyfL+/XscOXJEZ1kOtEF6ejp8fX0RHByMX3/9FcuXLy913Y+kOoQknFwoFKrVdww+lxzIh89qtasz7Oxw4fZtxAHY0LIlwOUWDOfJkJkrmZuTqLnTwPu7QJMujFRzVJGdnY2FCxfC3d2d1mFBZZFXc/KFnLXJvn378Oeff6Jbt26lb6xH6P4sM4w3b96Ax+Ph4cOHjFBzsgiFQsyfPx9OTk4qZSfXtZNWFlk1N3PmzBLVnDzy4eTqHrMxGpao8IzRUK12tUWh4Z6TJ/F1505sARBRoULBvJ3M2/oT6dzcJ6RLclqK84H2I1C1z3S9UnPq2LdixQrY2Njgp59+osEi5VC2kLMi6Dond+7cwa1bt+Dn50dL+5qi9dRi2dnZSEpKKnKhPH/+nLLs8tokLy8PYWFh8Pb2lqq57du3M+4mX7duHebNm6f17OR0oo6ak+fZs2eUhZObYiQcofhGJwDMMFLjPuhE4vA4Hz9CPHs2rADsA1B9926ge3epmnO+GY/b8mru9/no3MYYVv0a4+/uP6JWlbL7PhwYGIjq1atj5EjdnE9VCjlrk5SUFKxevRrBwcGMe/5RAlGRwMBA0qRJE9KpUyfSsWNHcuvWLel3Xbt2VbU5rZKamkoAkNTUVEIIIVFRUWTlypVk6NChxMnJiaSkpOjYwuI5deoUsba2VmtfoVBIhEIhxRZpxr1794ilpSUZNWoU8fb2JtnZ2Wq1k5GRQQYOHEg+f/5c6HNNjtmVnCQGZAAxJAO//zuAGJABxJWcVKs9bZGRkUGMjIzID0ZGJL9fP7INIFyAkHHjyOMPaWRB4GtSc9Vlgom7CX4ZTND6L4Jx20m1FReJud9Lcud9KhGLxbo+DLVQ5Xy/ffuWDBs2jOTl5dFsVWHy8vJIUFAQGTduHDExMSHXr1/X6Pem+r4Wi8VkxowZ5ObNm5S1SQeJiYmFnuOqoLLD69y5M/n69SshhJC7d++S9u3bE29vb0IIIV26dFHZAFU5fPgwMTY2JpUrVybdunUjV65cUXpficNzdXUlY8aMIWZmZuT27duMv8k/fvxIBg8eTLKystTanykOLy0tjRw9epQMHTqU2NjYkBcvXmjcprm5OTl//nyRzzU95igSR1YTZzKdOJDVxJlEkThNzNQKEoe31ciIXAPILICkNWhMhmy+QGAZStDfiqBpN4K+pgTmgaTLznvkyLWPJDVb99dGqbxOJ2T1c0Km3yv493V6oa+VPd+5ublk6NChJDo6miZDi/L27Vtia2tLBg8eTA4cOECSkpIoaZfq+9rJyYk4OjpS1h5daNXhtW/fvtDfCQkJ5I8//iAODg60Kzw/Pz9SsWJFwuPxSGRkJFm6dCmpXr06ef/+vVL7Sxze7t27Ga3mZMnPzyejRo3SyDno2uHdvXuXWFhYkNGjRxMfHx+11Zw8np6eZN26dQq/0/Ux64KMjAwyqlYtEl+jBhkAkG/gkHZ/Lib4ZRBB6wEE43bop5pzeU+IQTghhhGF/3X9775X9nwvX76chISE0GktIYR6NacIKq/xhw8fkgkTJhCRSERJe3SiicPjEKLaooYBAwZg//796CSzjicvLw9z585FYGAg8vPzKRxwLUzv3r3RrVs3HDlyRPpZu3btMH78eGzbtq3U/dPS0mBkZIT4+Hi9CbXdsmULWrRogRkzZqjdhkgkAgCtJpZOT09HQEAAIiIi0KFDB5iYmKBNmzaUtR8VFQVbW1v4+fkpjLDTxTHrmszkZGR06oYl6clokZ+PcKOfENt+GNBhBDq1bgbTnvUxtVNd1KqiP78J500Wqna7CY7cskgCAAZA9sO+IC2rKXW+T5w4gYsXL2LXrl202RsdHQ13d3fcv38fI0eOxPTp02mbm6PqGk9PT8e0adPg7u6O+vXrU2EarSQnJ6Np06ZITU1V+TmutMNLT09HzZo18eHDB1SoUAENGxaNVrt+/Tp+++03lQxQlry8PFSrVg2BgYGYMGGC9POlS5fi0aNHuHz5cpF9cnNzkZubK/07LS0NTZs2hZGRETgcDkiBwpVOzsr+f6BwNJBYLFa4HSGkUCoi2Z9TUduybUq2Lc6G/Px8CIVCad2p4raTb1N+O0mUaVpaGq3HRAhBfn4+8vLyQAhBxYoVpVlg5G0t7dhLOiaxWIzs7GxUrVoVBgYGCo+pVq1aIIQgPT2d9vNExTFpeu1JfnsDoRA/cQwxs0Er7B6/FYi+CfL8NDiJb/XumABgXfZkLMkdiQoo+lDPhwgHK5/CxqqB0vOdlpam0AbJNSObC5KqYyKEQCgUIi8vDxwOB5UqVYKBgUGhc0PHtVerVi1wOBzpMatzTIQQZGdno1KlStIXR10/90q79mrWrImPHz+q5fCUDsP6/fffcfr0aTRpUnyWCbqcHVBQxFMkEhVJ/dOgQQN8/qx4bdS2bdv0tpSFWCxGbm6uXiRrJYQgLy8PQqEQBgYGqFy5ciFHpOIgQqnk5ORIHyrlHbFYjLy8POTn54PD4cDQ0BDkzzkQJH4BfCwAYfb3FFr6GXHXTFwPnGIXihR8XxqSh3rVqlWlD3kqEIlEEAqFEIlEqFixovQFTNKnPiC5Z5mwDlEbKH2UPXr0QO/evXHmzJlCYeMPHz6EnZ0dTp48SYuB8siHysq/cclia2sLGxsb6d8ShffixQtGD2mKxWLMmDED69atw6+//qpxe5JhZiovakIIHjx4AFdXV3z58gVTpkzBuHHjULlyZcr6UERoaCju37+PzZs3l7gdHcfMFMRiMS5fvgx3d3eIRCLMnj0bPXr0wIwZM/D06VN8ue2PV69e6cXLUmlUtH8Dg32xgKioAzE0NMSYJdPwwcGuxPO9YcMGdOjQAVOmTNHYHklOS39/f/zwww8wMTFBr169dBLCr+k1/uLFC9jb28PX11cvhv4zMjIQFBSEwMBAfPz4Ua02lP6l+Hw+HBwc0L9/f4SFheHHH3/E2rVrERwcrJUUV/Xq1YOhoWERNff169diE75WrlxZ4QO4evXqjH4YbNu2DePGjUPv3r0paU+SdYSKJNNpaWnw8fFBSEgIOnXqhNWrV+OXX37RuF1lePfuHby9vREREVHkWKLwFS64jRgkwRh1MFvYHa1Rv0wl1v7y5QtcXV1x/vx56Vx648aNQQjBrFmzsGnTJkycOBEA869xpbFqCex9r/ArDgEqzW+JStWrF3uNnzlzBmlpaTAxMdHIDEkh53v37mHcuHHStF+6RJP7OisrC6tXr4aXlxejX/6B/0p/xcbGYsaMGfDy8kLTpk3Va6zEkBYFbN26lVSpUoVUrFiRjB49mty/f1/VJtSmV69eRdaitWvXjqxevVqp/eXX4TGRq1evklmzZlEa0ZWXl6fRmiOxWEzu3LlDzM3NyejRo4mvry/JycmhzD5lKCmc3IXcJAZkKTEky/77V7yU8IXXtWojHYhEInL27Fkyffp0MnXqVHLq1CmSn59faJsjR44QR0dHkpGRQWrXrk1q165NMjIydGQxDbiWHqWp6BqPj48nAwcOJJmZmWp1m5ubSwIDA8nYsWOJqakpuXnzJqMiWzW5ry0tLcm5c+cotog60tPTCZfLJUOHDiXLli0jz58/l36XkJBA/7KE+Ph4snjxYlK1alXSrVs3Uq1aNeLl5aVyh5ogWZYgEAhIZGQkWbZsGalevTqJiYlRan+mO7yEhAQyYMAAyu1TN3w5NTWVHDlyhAwZMoSsWLGCvHr1ilK7VMHGxkZhOPlr8oUYkKUEZEnh/8RLiIF4KYkiX3VgreZ8+vSJbNu2jQwaNIhs3ryZfPz4UeF2suHkGRkZpFatWqRWrVply+ERQkiU3Dq8qJLX4eXn55PRo0cXelAqy5s3b8iqVavIkCFDyKFDh0hycrKm1tOCuve1t7c3sbOzo8Eizbl//z6xsrIio0aNIl5eXgqXMGllHV6VKlVIly5dyPHjxwkhhJw+fZrUqlWLbN++XeVONeHw4cOkefPmpFKlSqRbt27k8uXLSu/LZIcnFovJpEmTaFHMqtwYTFBz8kRERJAlS5Yo/G41iSCGZFlRh0eWEEPxMrKaRGjZWvVRRs3JkpaWRgYMGCBNBCFZeG5kZFT2HF4pyF/jDg4OxNXVVen9c3NzSUBAAGPVnCLUcXivX78mI0eOZNQa1bS0tEJqLjIyssTtNXF4Ss/hubq6Yvr06dK/hw0bhosXL2L06NF4//49nJyc1BtTVZEFCxZgwYIFWulLm+g6O3laWhq8vb0RGhqKzp07499//6V03Zy6xMXF4eDBg8VWh4hBEkgx9Q0ICGKQRKd5lPD582e4ublJ5+b27NmDRo0albgPIQSLFy+Gvb29Xqyd0iaXLl1CdHQ01q1bV+q2ui7krE1ycnKwYMECuLq6MiKYS76QsyrJ4tVF6aOWdXYSunXrhhs3bugsAWtZQVfZyQkhuHv3Lng8Hr58+YK///4bx44doz3SUlmEQiEsLS3h5ORUrE3GqPM9bL2o0+OAA2PUodlK9RCLxfjf//4HFxcXiMVimJqaYuXKlUovtXBzc0PLli3x559/Fvqc6Ek4PF18+/YNGzduRERERLGRk7Klv+rVq8eY0l90s3LlSixbtqzEpWV0o2whZ7rQ2M0bGxvj+vXrVNhSLtFFdvLU1FT4+PgwTs3JY29vj7lz56JVq1bFbmOK3nDE/4p+QQoUnhn60Gih6nz+/Bmurq743//+h4EDByql5uSJjIxEaGgoQkNDi3xX1h/aJSEWi2FpaYm9e/eiRo0aRb6XV3NMKv1FNyEhIahUqRJGjRqlk/5VKeRMJ5ToWiaUtdBHCCFYsGABtm7dSvtvSAjBnTt3GKvm5Dlz5gySkpIUjizI0ho/QoAZMIMvOOCAgEj/5YqnopWh7of7xGIxzp8/DxcXFwDAvHnzsGrVKrUWzmdlZWHx4sXw8vLSi7VT2mTPnj0YNmwYOnfuLP2MqYWctUl0dDS4XC4iIiK02q9s6a8OHTqoVfqLanQ/kFuOOXr0KLp27Yo+fehTIampqfD09ER4eDi6du3KWDUny6dPn7Bz506lq7qboDf6owUEuCVdhzdX1BOtUHoWDjqRV3N79+5VWc3Js3z5cqxevbrYdsrrkOaNGzfw+PFj+Pj4AGB2IWdtkpeXB2traxw5ckSlotGaoEkhZ7phHZ6OePToEc6dO4egoCDK25ZVc1+/fsW0adMQGhqqcJiHaYhEIlhaWuLgwYPSHKLK0Ar1sQ1jpH8LibDYYBY6oVLNyePj44N69ephyJAhxW7DiHRrUfmASzYQIwKMDQHTqkBr+h41SUlJWL9+PXx8fBAYGMj4Qs5UoczLzZo1a2BhYYGff/6ZVluoKOSsLJq81LEOTwekp6fDxsYG/v7+lD6gUlNT4e3tjbCwMHTp0gWrVq1C69atpRkZ9IEtW7Zg8uTJWp3IpgI61JwsUVFR8PLy0vqwlMq4ZgHmaZDGEXEAOGYCglqASTXKuyPfs8w0adIEc+fOxYQJE8qtmpPn+PHjyM3NxaRJk2jrg8lqThGsw9MyVIeTy6s5ps/NlcSlS5cQExOD9evX69oUpZBXc6amppSpOVkk4eQuLi6MCCcvlqj8AmcnVvCdWRrQvxLQihr78/LyEBYWhk2bNqF69eqws7NDz549tTZsx3Q+fPiA/fv3Kz0toArp6enw8fFBcHAwOnbsyIi5OWVh8N1TNikunFxVZNVc165dpWpOEfowpPPt2zds2rQJ4eHhlLRH5zF//vwZLi4uuHDhAgYNGkS5mpNn5cqVWLJkiVL5A3U6h+eSjWILG3AACLKBbTU16iIqKgo8Hg+PHj1Ct27d0KpVK4SEhEhrw5UnirvG8/PzYWlpicOHD1OqtiRqLj4+HjNnzkRERIRO1Jwm9zbr8LRISeHkyiBRc1wuF9++fcOsWbP0Vs3JIhaLYWVlVWw4ORMQi8U4d+4cXF1dweFwMG/ePKxevZr2ObOQkBBUrFgRY8aMKX1jXRMjUrQcsgDy/Xs1yMvLQ2hoKLy9vdGgQQNYWFhgzZo1mDhxIoKCgvTihU6bbNiwAbNmzaIkOE2i5kJCQvDrr7/CxsZGa8ni6YB1eFpCk3DylJQUqZrr1q0bVq9eXaya00dWC/Yia91obOuUCmM8hClaojWYkcH906dPcHV1laq5ffv2KSx+TAfR0dFwdnamZViKFowNS1Z4xqpd97JqbsKECfD09ISRkREIIZg9ezY2b96MOnWYmVhAV5w7dw5fv34ttXxWady7dw9cLhefPn3Si7k5ZVG64nlZIC0tDUZGRmpVytUUKysrTJ48ucQIO1kIIbh9+zZ4PJ5UzY0fP16tOQom14aze3MGW1t8hSHHAITz3xo6AfrCBC3VbleTY1ak5gYPHqzVCMi8vDyMHTsWR44cUTrCLjMzE40bNwYAxMfHa788UFQ+0DZB8RyeAYBX9Uqdw8vNzUVYWFghNdezZ89CKo7L5SI5ORmrVq2Sfsbka5wu5I/58+fP0jn8atVUDxBKS0uDr68vQkJC0LFjR1hYWDBSzSUlJaFu3br0VjxnUR9lwsklyKs5W1vbEjON6DN3U+Kw9ecvgIEBRNKxsIJ/zXAT/fEjWkGzOR9V0KWak8fOzk6tcHKdDu+1rlAQjWkmF6VJUPB5Cc5OXs0VV6ftyZMnOHXqFIKDg+k6Cr1EspznwIEDKjk7Qoh0bk6i5iIiIvR+mqQ4WIdHM8qEk0vUHJfLRWJiImbNmoUTJ06U6YgzQgjmXOTDcHxrKJrZ4YADAd5gG7rSaodEzbm4uMDAwACmpqZamZsriRMnTiAnJ4fWcHLaMKlWEI0pkFmHZ1ZVobOTV3OWlpbYsWNHsU47IyMDy5cvh6+vLzPWGzKIbdu2Yfz48ejQoYNS20sKOYeGhqJTp074559/GKnmqIZ1eDRSWjh5SkoKvLy8EB4eju7du2PNmjVlVs3Jc/DgQVQd1gykGEFCAMQgg7b+4+Pj4erqiosXL2Lw4MHYv3+/ztScLB8+fMC+ffvUnrdjxAxFqwolRmO+fv0aPB4PT548KVHNybN06VKsW7cOP/74I5XW6j1XrlxBVFQU7OzsStyOECKdm5MMf5ZlNacI1uHRiKJwckIIbt26BR6PV27UnDz37t3DtWvXMHTxajzBCyiudAAYg9qITbFYjLNnz8LV1VWq5mxtbRmjFvLz82FlZaVRODlTIxZzc3MRGhoKHx8fNGzYEBYWFnB0dFTaXnd3dzRr1gx//fUXvYbqGd++fcOGDRsQHh5e7G8pr+b0Ib0gXbAOjybkw8l1qeYY8db/ndTUVKxcuRJBQUFI5FTATkQq3K6g0oH6v4/sMTNVzcnj4OCAv//+W6OHEdMcnrpqTpaXL18iKCgIYWFhxW7DpGtcW4hEIlhbW2PPnj2oWbOwopaoOR6Ph8+fP5epuTk2tRjDkISTR0RE4ObNm+VazclCCMHChQul4eR1AAjQF2a4+T06UxLjUBClqUnAikgkwvnz5+Hp6clINSfP+fPn8eXLF2zatEnXpmiMRM15e3ujUaNGKqs5WbKzs7Fo0SJ4eHiw1SHk2LdvHwYNGoQuXbpIP5NXcytWrCi3ak4RrMOjmLy8PFhYWKB///4YPXo0evToATs7O7RsqX6IfVmBx+OhY8eO6Nevn/QzE7REf/wIAd4gBhkwRg2YoZXazk6i5iSRlgcOHECDBg2oOgRa+Pz5M7Zv3671PJnCKCDTBRDFAIbGQHVToKIGyztfv34NLpeLp0+fYuLEifD29tZ4+Y+NjQ3+/fdf6XILlgJu3bqFBw8ewNPTs9DcnKT0V1lRc5RDyhGpqakEAElNTaW8bbFYTG7cuEF+/fVX0qNHDxIYGEhyc3Mp70cdhEIhEQqFOrXh8ePHZPz48UQkElHedn5+Pjl58iSZMmUKmTFjBjl37hzJzc3V+TErQ35+Phk7dix59uyZxm1lZGQQIyMjYmRkRDIyMkrcNt2FkFgDQmINC/+b4apanzk5OcTHx4eMHj2aWFhYkLt37xKxWKz+Qcjg5+dHVq9erdS2TLjGtUVSUhIZMGAAefv2LTl48CAZMmQI+ffff8mrV690bZpWSExMVPs5zi4815CUlBR4enoiIiICtWvXRpUqVeDp6UlJ21Sh60W5GRkZGDduHHx9fSmNsIuPj4eLiwsuXbqEIUOGwMTERKrmdH3MyrJlyxY0atQIpqamGreVmZmJn376CQDw8ePHYheeC6OAz21R7ALxhq+AiqVMn8qruRkzZlCazOHt27dYvHgxwsPDUbFixVK315fzrSlisRjDhg1DtWrVIBaLMWPGDEyaNKlcqTl24bmWIYRI5+aSk5Mxa9YsODs7w8rKSn/SQGkRKsPJRSKRNNKyQoUKMDU1xZo1axg7N1cSV69exevXr7FmzRrK2lTm/TXTBSWmAMsUALW3Ff0qNzcXISEh8PHxQaNGjWBpaYldu3ZpZK8icnNzYW1tDT6fr5SzKw+kpqbCx8dHGnC1c+dOtGjRAkDZd/JUwv5SKpCcnCxdRN6jRw+sXbsWLVu2RH5+PsaNG0d5dvKyAFXh5PJq7uDBg4yfmyuJhIQEbNiwAWFhYZRGVirTligGJSZ5FsUU/ujVq1fg8XhSNefj41MkKpBKVq5ciUWLFqFZs2a09aEPEEJw9+5d8Hg8fPnyBf369UP79u0RHBwMDocjVbUsysM6vFKQV3OzZ88uEmlJRTh5WSEKeXBBKmIgRI2ENLy5fgnnj/DVaqssqTlZxGIx5s+fj927d9PqOIrD0BglKjxD48JqrnHjxrSpOXnCwsJgYGCAsWPH0t4XU5GoOUkh55UrV6JBgwYYP348AgMDGbf0RJ9gHV4xyKq5nj17Yt26ddIhBFnKUji5prgiFeb4XLC0gADiH8QwcF4NT04GTKB8Beqypubk2bt3LwYOHFgonJwqlBnSrG4KpDsWv/+BL9twfexlrag5Wd6/fw8nJyccP35cK/0xCSJXyHnWrFnSSEtCCObOnYuNGzeibt26ujZVr2EdngyK1NzJkyeLnUfQVTg5E4lCHszx+b84CA4AQ0OIAZjhM/qjKlqh+PWHsmquYsWKZUbNyXP79m3cv38f3t7etLSvzNt/xdZAHQGQZAZI3k4ICIgYOP67B0YtHIb13ambV1QGoVAIKysrHDlypFytU1WmkLNAIEDbtm3Rv39/HVlZdmAdHpRXc7KIRCJYWVlh//79apXiKGu4ILXkYtdIxTbUL/Ldx48f4eLigsuXL2Po0KE4dOhQmc2VmJycDFtbW4SEhOh8WKq6CfCh0Vs8XxcDcZwB6nWpjS7bWmNhFxOd2LN27VqYmpqWi/Wqsmru27dv+Pvvv3H8+HGFjv7Zs2c4duyY2kWjWQpTbh2eqmpOnu3bt2PcuHFKZyfXJdpYeRIDYcnFriGU/i0SiXDmzBm4ublJ1ZydnR2lao5pq20IIbC2tsb27dtRu3Zt2vopzZHm5OQgJCQEvr6+BXNzRyzRvXt32uxRhlOnTiE9PR1Tp05Vuw2mnW9FKKPmZMnMzMTSpUvh4+Oj8N7Qh2OmA02Ou1w6vKNHj+L8+fNKqzl56Agn13eMUREcSW4wOTjfvy9Pak4eJycn9OrVC7169dJJ/y9fvgSPx8Pz58+1PjdXEh8/fsTu3bvL7HIeiZrjcrlISEjArFmzilVz8ixduhRr1qwpU/PXVHD79m219y2XDq9x48Y4ceKEWmt86AonpxNt2GkKI+wgCQA4gGx/BBCD4NGStfg3MR1mZmaUqzlFMOncPHz4EBcvXkRgYCDtfcm+/UrUnI+PD5o0aQILCwudqzlZJNUhDh06hKpVq2rUFpPON1Cg5ry8vNQu5Ozp6YnGjRtj0KBBxW7DtGPWBomJidi2TcEiUWXRLMmLfqFpajGRSEQmTZpEHj58SK1hNKONtEuhoaFkiPcRYkBeEkPykhiIXxKOKJIgP5JMPeFLvnz5Qmv/8jAl1VRaWhoZMGAASUhIoL0vSWqxGjVqkEWLFpFhw4YRLpdL0tLSaO9bHdavX088PDwoaYsJ51ssFpObN28SU1NTMnbsWBIQEKBWesGXL1+SUaNGlXo8TDhmbSIWi8nkyZPJ//73P7Wf4+VS4anLnj17aAsn12ck4eTh4eHwungVu1NikNOgLvo1bo4NzX5Fm5HtdG2iTiDfq0OoG06eEQXEuQDZMUBVY6CpKVCjmCmfnJwc+Pv7IzMzExwOB9OmTWN0VN+FCxfw4cMHODg46NoUjUlJSYG3tzfCw8PVUnOySKpDuLm5sRlU5Ni3bx/+/PNPjZ6/7C+qJLdu3cL9+/fh4+Oja1MYhVAoxNy5c9GlSxeMGTMGw4YNw5W5c8vN3FxJuLi4qB1OHucKPDYvGB0mpODft45AZwHQ1OS/7V68eAEej4fIyEiMHj0a1apVA4fDQdeuXak7EIr58uULtmzZotfLeQghuH37Nng8nspzcyWxYsUK2NjYSHOishRw584d3L59G76+vkhMTFS7HdbhKUFycjLWrFnDiHBypiASiXD69GnY2Nigfv36GDt2LPbs2VPm1s2piyScPCQkROV9M6IKnB3E/2UAk/z72Ayo3jMXpx4FwdfXF02aNIGlpSW6deuGzMxMrF27lqpDoAWxWAxLS0vs27ev2OTWTEZeza1Zs4aypRSBgYGoUaMGRowYQUl7ZYWUlBSsXr0ahw4dwtatW3HmzBm122IdXikQLYWT6wsfPnyAi4sLrly5gubNm6Nfv35wdXXVtVmMorRw8tKIc/mu7BR8JyYiHBwThsa2WfDz80ONGjUKfU8YHqq+Y8cOjB49Gh07dtS1KUojq+YkhZypUHOyvHv3Di4uLnqteukgPz8fEyZMgKGhITZt2gRTU1NYWVmhfv2ia3qVgXV4pXD48GGdhpMzAYmaO3jyNOL+HIIGs63Qfv4yPPhnMf7HPapr8xjHsmXLNAonz44pGMZUhAHHAGN6T0M3C8XfM3kE4tq1a4iMjISHh4euTVGKlJQUaUKK7t27U6rmZMnLy4O1tTW4XC5bHeI7kvSCXl5eaNGiBVxdXaX3U1JSktrtsg6vBB48eIBLly5pJZyciXz48AECgQBXr15F3SUrcG7LAXA4HLwEwSWRGJyDbvA35MBE14YyCC8vr1LDyUujqjFQ3KJGDodT8L2ekZiYiPXr1zN+OQ8hBLdu3QKPx0NSUhItak6e1atXw9raGs2bN6etD31APln8H3/8gfbt2yMoKIiyqRLW4RVDWloaVqxYUSayk6syzCUSiXDq1Cm4ubmhSpUqMDMzwwy79WiXyZGpF8oBDA1BAJhlA/0NgVaGNBiuAboY2nv9+jX8/f0RFham1v45OTkICgrCqVtXMF189Lu7K3ztEQI0Myu+DSZeq4QQWFlZYdeuXZQWiZXvQxPk1ZydnZ1W0pxFRERAJBJh/PjxKu/L9OFrZVGULL5atWoYP348/P39izg7TY6bdXgKIIRg0aJF5So7eVxcHFxcXHD16lUMHz4cR44ckY6T2+aUWE0GAiGwjWEOT9vk5ORg0aJFcHV1haGhaj9GZGQkeDweXrx4gcmTJ8P52B4kBxngsVnhKE1CCqI0q6sX8a4zJOHk3bp107UphZBXc7Nnz6ZdzckSGxuLQ4cOldksMyUhr+bMzMykyeIJIZg3bx7s7e1Rr149SvtlHZ4Cykt2ckVqbv369UVUQoxYcQAF8D1PpriYL8sRK1aswPLly5UOJ8/OzkZwcDB8fX3RrFkzWFpaFlpKUMMEqNMfiBX8tw6vmZn+Obs7d+7g1q1b8PPz07UpUiRqLjw8XFrIWdX0gpoiFAoxf/58ODk5oXLlylrtW5fEx8dDIBBI0wsqKv3l5uaGVq1a4Y8//qC8f9bhyVEWs5PLO7C4uDgIBAJcu3YNI0aMKKTmFGFsAHBQzJzS9++ZhjaH9gIDA1G9enWlwskjIyPB5XLx8uVLTJkyBf7+/kUiLSVUbwW0UzGLEpOGuSTh5JIK3XRSWvuK1Jx8IWdtYm9vjzlz5qi9QB1g5vC1IlRJFh8ZGYnQ0NASn7+aHDfr8GTQNJycyeTn5+PUqVNwd3dHlSpVYG5uDnt7e6UuHtOKwI5sUuDd5LYnAMzKcWDZo//F4uwqMQb33IZztkA3U6CuXDaU7OxsBAUFwc/PD82bN4eFhQVtC8OZ4vAIIViwYAG2bt2KH374QWd2yJf+0oWak+fMmTNISkrC9OnTdWoH3aiaLD4rKwtLliyBl5eXytMCysI6PBnKYnbyuLg48Hg8XL9+HSNHjixVzSniy81r6PMoErdnWxTUCwWk/wqqMi9gRVvc5eXjmGUT/GQ4FS/ecwAOcN0RGCcAupr8p+ZevXqFyZMnl6jmqIIpb/1Hjx5F165d0adPH633TTQs/UUnnz59ws6dO8vsvJ0mpb+WL1+O1atXo2HDhrTZxzq87yiTnVxfkFVzVatWhYmJCdatW6fWDS8JJz8dFoav1TkQCAvm7IwNCpRdeXV2iVHAMSsDcGAAIpL9hiDMFNjkZoGG7SvB0tKy3OVeffToEc6dO4egoCCt9pucnAw/Pz+VCjlrE5FIBEtLSxw8eFDj6hBMQ9PSXz4+Pqhfvz4GDx5Mo5WswwMAvHr1Cn5+fggPD9e1KRohPzd39OhR1KtXD/n5+Wq1Jx9OXgtsNKaEANsoAIoephyAI4Z5dyeM3K39+SFdD2mmp6fDxsZGYTg5HUjUnLOzM1JSUjBnzhzGqDl5Nm/ejMmTJ6Ndu7KRTF2SkMLNzQ2VKlVSu/RXVFSUNF0b3ZR7h5ednY2FCxfC3d1dL7OTS9Scm5sbqlWrptLcXGnYObkhdfJq7KzYDcZvANPGQOtqFBit58TGxuLZtQ+oz2mlMCMKBwbIjNdNMIQuhzQJIVi8eDHs7e3VTv2kLMnJyfD09MSxY8fQq1cv2NnZoUWLFoy9hy9evIiYmBjY29vr2hSN+fjxIwQCAa5cuYJhw4bh8OHDaieLz8nJwYIFC6TLE+iGmVeHFtHX7OSxsbEQCATSuTlnZ2dK16ysu/YO21rPhaEhB+RLQayKYwwgaA+YNKasG71DKBRi1qxZ6Fp/JcRfxeBAgeTlALWNtW6aznFzc0PLli3x559/0tI+IQQ3btwAj8dDampqobk5dUcxtMHXr1+xadMmvc6TqUjNrV27VmMVv3LlSixbtgxNmjShyNKSKdcOTxJOPnLkSF2bohT5+fk4efIk3N3dUb16dZiZmWHDhg2Uv9Xf/5yGzVnNAQMDiOTS9ZtFAv1rA63KmdLLzs5GYGAgNm7ciJ9//hlTNrfA+YmGinNeEqBbCdlQyiLKhJOri7yas7e3x88//0x5P3QgFothZWWFffv20R6wRAeyyeI1VXPyhISEoFKlShg1ahQl7SlDuXV47969g0Ag0ItoKU3VnCrzOoQQzPa+CMPOYyFS8D0HgCAe2MbwBdBUzWU9f/4cXC4Xr1+/Rrt27fDnn39CIBAAAKoLgHAzQD50dZwAqKuj30cXQ5pZWVlYvHgxpeHkEjXH5/ORkpJSaqSlrucui2Pnzp0YPnw4OnXqRHnbdB0zXWpOlujoaHC5XLVUL5taTEUk2cmdnZ0ZObkNFFZzkrk5OtScPEePHkXlZn+BFJNMjACIyabVBNr4GAWcdQG+xgA/GgNDTYGfFFQQl6g5f39/GBsbw9LSEj/++CNmz55d6AWpqwnQrD/wQACkxBQMY3Yz052z0xWScPJGjRpp3Ja8mlu/fr3eqDl5bty4gadPn8LT01PXpiiFJFn8lStXMHz4cDg5OdEyFyt5/h45ckTrC//LpcOzt7fH/PnzYWxsrGtTihAbGws+n48bN25g1KhRlM/NlcSjR49w/vx5DNs+H09joTCfGAeAsR5GVJ91BfbLVRAPcgSWCYAhJgXbPHv2DFwuF1FRUZg6dSoCAgJQvXp1aXJfReHkdVsBQ1TMhlKWkISTDxkyRO025OfmmBxpqSxJSUlYu3YtQkNDGbM2UhGyaq5y5crFphekEjs7O1hYWOjkRUZvHN6WLVtw4sQJPHr0CJUqVUJKSorabYlEIkyYMIE64zQkPz8fJ06cgLu7O2rUqAFzc3M4ODhQdtEp0056ejr++ecf+Pv7I7kaBzvfK96OADDTg6AV2WP+GFXg7IiCCuL7zAhefQ3FyUt8/Pzzz7C0tETnzp0LtbVlyxa9CScXi7WX2FTTcPLk5GR4eHjg+PHj6N27t0Zzc0xyKoQQzJ8/H46OjjAyMqKtH02OWbb0F51qTp4TJ04gJycHkyZNUruNcpFaLC8vD1OmTEHfvn2lcyjqsmnTJoqs0oz3799DIBBI1RyPx9NJdQbZcPJ69eqhHgqiMc0iC5SQOBvAN4DkAcMbAyQHgB4FrZwtoYI4IWK8u9xKGsAkz6VLlxATE4P169fTbygFaOvBr244OSEE169fB5/PR1paGqOyoFDFgQMH8Ntvv6FHjx66NqUQyiaLp4sPHz5g3759Oo2b0BuH5+DgAKAg9FlTdJmdnG41pw6KspObNC6Ixlx6HTj5tMBhGAA4kwy0fQ4IRgIm1M/D08LXmJIqiBuiQa1OUODr8O3bN2zatEnvExLQgarh5ElJSfD09KREzTGZe/fu4fr16/D399e1KVJKKv2lLfLz82FlZQUnJydUqVJFq33LojcOTx1yc3ORm5sr/TstLQ1AwVoqoVCoVIZ1CSVtq8x279+/h4uLC27duoURI0bAyclJOjcnEimKh/yvXU3tlF2jJL9tZGQkQkJCEBQUVGS7vAzg9P0KADggRFYhEZidBPo0EqHVD8r/TuoeU/QbDnzdDBD3HmjaHJhhIkaL1oq3lbRbaF1W1UQQUg9QuGaOoF4zgvz8wkOBIpEIFhYWcHR0RJUqVUpc50XVeVJnW9nt8vPzUbNmTan98jZTdZ5CQ0NRoUIFDBs2DEKhsNg2JWrOxcUF6enpmDlzJsLDw1GxYkVwOJxif1N17CzuHlL2mDTtHyh4vvz777/w9/cvYg8d517y+xFCimwnmZvz8PBA5cqVYWpqCltbW3A4nBJ/e1X6V+WY1q1bh+nTp8PY2LjUNZOlnSdN1lyWaYe3bds2qTLUBRI15+XlhRo1asDMzIyyLChUkJWVheXLl8Pd3V1hOLnbU4NiYjU54IDA9akBtvxB75yRnzsH/1gZFgo2ObzLEHu4YkyfW3x4clZWFkJCQhAcHIwmP/QCh7Ph+40ke0QEhABD5hU9hj179mDo0KG0hJPTCd3XVnR0NPh8fonr7ZKSkuDl5YWTJ09KIy2NjY0Zu3SACiRFox0cHFCnTh2d2REXFwdXV1dcv34dw4cPx6FDh1C/fn2d/vbnz59HQkICI6pD6NThbdiwoVSHdPfuXbXHwm1tbWFjYyP9Oy0tDU2bNkXFihVpnTN4//49+Hw+bt68idGjR4PP5zOicrr8XMuiRYtga2tb7LBUXHpJhV85eP6Rg3WBBoj5BhjXB0z/AlprHpku5W0U8I8VoCgOw8bSEP3+BFrILQF4+vQpuFwu3rx5g8mTJyMoKAjVq1fHuaHAvu8VxCVr5gjhYJkAaNa28O9y48YNPH/+HJ6enox5OVGGChUqSEcxDA0NKU/VlJeXh8WLF+Po0aOoVq3wJC4hBNeuXQOfz0d6ejrmzJmDU6dOaW1uTnKedJVazNnZGV26dKGlaKkyyJf+0vU0iYTPnz9j165diIiIoOxa0OQc69ThLVq0qFSvr8nSgcqVK2ttvk4oFOLEiRPw8PBAzZo1YW5ujo0bNzLiolOEMtnJjWsrKvlaAEkETj4GTssoL8cIQGAFmPxVdPuoaMAlCIj5ABg3AUwnA61LmcLxcSlSfk8KhwN4C4B12wrUXEBAAAICAtCyZUtYWFigffv2AP67OYaYAB36A2cE/63DG2YGNJZzmPoSTl4cdL7JKwonT0pKkkZa9u3bFw4ODoxc7kMnT548wenTpxEcHKzVfiVq7saNG0oVctY2kuoQBw4cKPKCpCt06vDq1auntTVmdBETEwM+n49bt25h9OjROou0LAn5h+Dr16+VCic37QQ43lLwRS5A4gr+b5HUY85A/7ZAK5mSVq5BgLlt4TVwjlxAsA0wmVx8/7ExxQebEAI8fZSCxYvX4e3bt5g6dSqCgoKkN5bs3JKExq2AeSWsmdNWODmd0FWhQDacXNdqThG6GrLLyMjAsmXL4Ofnp5XqELKlvypXrox58+YxRs3Js23bNkyYMEH68kkV5SLTSmxsLJKSkhAbGwuRSIRHjx4BAFq1aqX1HHVCoRDHjx+Hh4cHatWqBXNzc2zatImRF508OTk5WLhwoVLh5K3rFERjmp0snD1LlAQYcACxooXpHEBwEdg2o+DvqOgCZ6doWNLMFujfA2hlrLj/ZsbFKzwxEeHT1ztY52iJjh07lngcynLw4EFGhpPrGkk4ubu7O/bt21eu1Zw8S5Yswfr16ynLL1kcikp/SV7KmPjcuXLlCt68eQM7Oztdm1IIvXF469evh7u7u/Tvrl27Aigou/HXX39pxQaJmrt9+zZGjx4NgUCg0wlqdfj3339VCic36QT0bwIIngAxKQXDnE/vAae+Kd6eECBG5juXoJKHJQWBwLZ/FX8/0xQ46KiwFxhwDODuP7TIHJ663Lt3D9euXWNUODkTEAqFmDJlCho2bIjFixdjzpw5OH36NGPL8GgTd3d3NG/enLbnT2mlvxSNYjCBb9++wcHBAWFhYYxzxnpz1bq5uVGyBk9V5NWchYWF3qg5CRJbg4ODUblyZZWzk7eqA2z767+/bT8Bpx9AceoxTkEAi4SYDyUPS8Z8KL7fRj9lYbLJfQS4/AYOh4DDMQCHwwEhHOwXFA1YKWyH8ucnNTUVK1euRFBQkF6dV0VQNbSXmJgIDw8PHDhwAJ07d8a+ffvQvHlzStqmA22ftxcvXiAoKAhhYWGUt61ssngmXqtisRjz58/H7t27pUtkqKZcZFrRNmVBzckiyU5ORZYD078KAlQUQQhgNuC/v42blKzwjBUIzSdPnoDL5SI6OhpTp07FomU9EOxTFbExBcOcf5uV7OxUgRCChQsXYvPmzXp9fqmAEIKrV6+Cz+cjMzMTnTt3xqBBg8Dn83VtGqPIzs7GokWL4OnpSVl1CG2V/qKbPXv2YPDgwejSpYuuTVEI6/BkkFVzRkZGejU3VxJ5eXlYuHAhnJ2dKclO3rpRQTSmmXPhQBRCCj6XDVgxnVwQoKIIQgCzKQX/PzMzUxpp2bp1a1hZWRWam2tPU4JmHo+Hjh07ol+/fvR0oAdI1NyJEyfQr18/bNq0CZUrV8bff/+tF+WztM3y5cuxcuVKNG6seVJZugs5a5Nbt27hwYMH8Pb21rUpxcI6PPy3mPb27dsYM2aM3qs5edauXQtzc3NKUzmZ/FUQjSm4COk6PLMBhZ0dULD0QLCtIECliHPcBmSlPcGiRVy8e/cO06ZNQ3BwsNZCmJ88eYJTp05pPZycTpQd0pRXc7Jzc5Lk6kwKJ2cKfn5++OGHHzBs2DC12ygrak6W5ORkrFmzBiEhIYw+jnLr8IRCIY4dOwYPDw/Url0bFhYW2Lx5M6NPljocP34cubm5mDhxIuVtt2r4XzRmSZhMLojGFAQWzNn91CAP9SpHwF8gwMM2bTB//nz8+uuvlNtXEhkZGVi+fDl8fX21Ek6uLUq7fhWpOfm5uW3btmH8+PHo0KEDnabqHW/evIG7u7taRUuB/9TcjRs39F7NyUIIgbW1NXbs2IHatWvr2pwSKZcOb+PGjXj8+DHGjBkDFxeXMqXmZPnw4QP2799fYhoobdHKGJg+9DG4XC5eXI/RupqTZ+nSpVi3bh3t4eRMgBCCK1eugM/nIysrC3Pnzi020vLKlSuIiopiXDi5rsnNzcWCBQvA5/NVWm8or+a0VchZmxw+fBi9e/dGz549dW1KqZRLhzd06FDs3LmzTF108uTn58PS0hKHDx/WaXbyzMxM+Pv7IzAwEG3atIG1tbXW1Zw87u7uaNasmdaWs2gT2SHNxMREuLu74+TJk/jtt9+wZcsWNGvWrNh9v337hg0bNiA8PLxM3xvqsHLlSixatKjE308W+ULOXC6XcQkpqODBgwe4fPkyAgICdG2KUpRLh9enT58yf0Nv2LABs2bNQps2bTTKLq4ujx8XqLmYmAI1FxISUqRauC54+fIlgoODGaF66UIkEsHc3Bx5eXklqjlZxGIxrKyssGfPnv+3d95hTV3/H3+rP1fVUq2tdS9atbXWulqtraLWUWerWGxxVAVRQHAhggX3QIoDFwkb2dvipHXVWqtWEQdSQQUBlaUgO5D7++P7Tb4xhpBxZ3Jez8PztPHmnM9Jbu7nvs953/NhzE4uVBISEtC4cWNMmzZN7XGyzeKDg4Plao6vu6DQQWlpKVavXo3o6GjBjNEoE56hk5ycjPz8fGzZsgUAe9suKau5ZcuWcbYOpGrMlZWVsLe3R3BwMG12cr5QWFgon7Js0qQJ3N3d0bdvX43fz3c7eUMwdY5nZWXh4MGDSEpKUnuMYiFnttQclxUQZNUhNm3axLpyNYqtxQia8fTpU+zYsYNVO/nNmzfh4+ODrKwsWFhY8EbNKbNy5UqsWbMGHTvSWNKBQxTX5iorK/H999+jVatWaNSoEbp27apxO5cvX8Y///yDsLAwBqMVHhKJBEuWLMGhQ4dee5yHj4Wc2cTPzw/9+vXDyJEjWe+7oqJC5/eShGdAsLk7eVlZmVzN9e3bF7a2trx29UVGRqJt27YYP34816HoTWFhIYKCgnDixIlX1ubKy8u1vuAKxU7OBevXr8fChQvRu3dv+WuKpb8mT57My83imeb27dtISkpCXFwc6/2KRCKkpaXp3AZJeAZEfXZyOi9kKSkpEIlEcjUXHx/PSzWnOObMzEy97OR8gKIonD9/Hn5+fqisrMT8+fPh4ODw2tqcNtM9Mjv5jh07eG8nbwi6k/WJEydQVlaG2bNno7a2Vr4hBZ9Kf3HRf3l5ORwcHBAWFsbK4zwVFRWIjo5GZGSkvPRXly5ddL7JIAnPQGDSTi40NaeIop1ciBseK6q5kSNHNui01IYDBw5g2LBhGDZsGC3tGQq5ubnw8vLC/v378fPPP8sLORujmlPGwcEBrq6u6NChA6P9yAo5qyr9VVxcrHO7wrsCEF6DKTt5SkoKfHx8kJ2dzWs1p461a9fCzs5OqzUtrtFUzdX3Xk24fv06zp07h+joaH3DNSgqKysxffp0tG3bFtu2beONmuMDISEh6Ny5M8aMGcNI+8qFnK2t6Sv9JYMkPIFDt528rKwMERERiImJQb9+/WBvb097AUe2SExMROPGjTF16lSuQ9EIZTW3bds2rRO1JhdmIdrJmebRo0fw8/NDaGgohg8fDm9vb4PdkEIX0tPTERkZ2WDRaF1Qp+bohiQ8gUOXnfzGjRsQiUTIzs7GnDlzBKnmFMnKyoKPj49aOzkfoCgK586dg5+fH6qqqrBgwQKN1Zyu/XFlJ+cbEolE/txcmzZtMGjQIJiZmcHPz4/r0HhFZWUlbG1tERQURNvjPGyoOVWQhCdg9LWTG5KaU0QikcDW1hb79++npToEExQWFiIwMBAnT57El19+ie3bt9My7drQlKafnx/69u3LiZ2cLyiX/vL19YVEIsEPP/wgaGMTU6xatQqrVq1C586d9W5LUc19//33jKo5VZCEJ1D0sZPL1Nzjx49hYWGBhIQETrcfo5v169djwYIF6NWrF9ehvIKimquursb8+fPh6OhIq5pTdy7cvn0bv/76q0HvMlMf6kp/SaVSfPfdd9i7dy9atWrFdai8IioqCm3atMGkSZN0bkNRzZmamrKm5lRBEp4A0cVOXlZWhpiYGLmaW758Ofr168dsoBwgs5PPmjWL61DkFBQUICgoiHY1pw1s28n5giaFnHfu3IkpU6Zwvscr38jMzIS/v7/Om1jcunULPj4+8kLObKs5VZCEJ0C0sZPfuHEDhw8fRk5ODn744QeDU3OKyOzkv/76K6fbLgGq1+ZWrFjB+JZm9Sk8BwcHuLi4MG4n5wrF71ubQs4XL15EWloanJ2d2QyXFpg8x6urq7F06VKIxWKtqkM0VMiZDsjWYkaEJnbyly9fIiIiArGxsfjwww9ha2uLfv36aXXiCo3a2losWbIE+/fvR4sWLSCRSDiJo6CgQL4299VXX2HHjh3o0qULJ7HICAkJQadOnTB27FhO42CaR48eITAwUONCzkVFRXBzc0NCQgJxqyrh7OyMZcuWvVYrsT5SU1MhEnFTyFkbSMITEA3Zya9fvw6RSIScnBzMmTNHrua4qJbANps3b4aFhQX69OkDgN1dKCiKwtmzZ+Hn54eamhosWLAAK1eu5GSDauW73/T0dERERDBiJ+cDioWcTUxMYG1trVEhZ4qiYGNjA09PT7z55pssRUsvTJ3jR48ehVQqxYwZM9Qep6zm2CrkrM+4ScITCPXZyWVqLiYmBh999BEcHR212iXfEDhz5gxyc3OxceNGVvvNz89HUFAQTp06ha+++go7d+7kXM0pomgnF+IuM+p4+PAhfH19ceXKFUydOhUikQjt2rXTeJx79uzBqFGjMGjQIIYjFRbZ2dnYv3+/2nW71NRU+Pj4yEt/8VXNqcKwfgUGjLKdXFHN/fDDD0hMTDTYtTl1PHv2DFu3bmXNTi6VSuVrc1yrOVUoKrzVq1dj5cqVtNjJ+YBMzYWEhOCtt97C4sWL5WpOm1mMK1eu4O+//0Z4eDiD0QoPWXWIgwcPonnz5q/8Gx8LOesCSXgCQGYnDw4OhkgkQmxsLPr372+Uak4R2S4zbNjJ+a7mZMime+Li4tCqVSt88803HEekP8pqzt/fH23bttWprRcvXsDZ2RmxsbFk3U4JNzc3zJ8/H6ampvLXlAs5C0nNqYIkPJ5TXl6OhQsXok+fPrC0tMScOXOMVs0pw7SdXCqVytfmJBIJfvrpJ16pufqQSqUICQnBsWPHuA5FZxTX5tq2bQsrKyuN1ubUQVEUli1bhm3btumcMA2VU6dO4fnz57CwsDAYNacKkvB4ysuXLxEeHo5NmzZh+PDhcHV1NWo1pwyTdvL8/HwEBgbi9OnTGDVqFHbt2iWYaUGpVIqKigrs3btXkK7chw8fQiwW4+rVq5g2bRoCAgJoS06HDx/GoEGD8Pnnn9PSnqGQl5cHDw8PbNu2Dba2tnI1x9dCzvrQiOL6gSUWKS0thYmJCUpKSnjrzPrnn38gEomQl5eHrl27om3btti6datebcrWNwzFuFBUVARzc3MkJCTU+z1qO2aZmvP394dEIsGCBQswYcIE3qs5RcrLy+XGjfz8fMHsGiKRSHD06FGEhITI1dzw4cO1UnMNfd8pKSnYvHkzoqOjDebBezp+16Wlpfjqq6/ke4laW1vzvvRXcXEx3n77bZ2u44ZxBRQ4MjUnW5tbuXIlgP/sYeft7c1xdPyCbju5sprz8PAQjJpTRjaFKRRl9+DBA/j6+jKi5hR5+fIlVq1ahcjISINJdvpy8+ZN+Pj44LfffsOoUaOwb98+g1NzqiAJj0MU1Zyi07KyshLTpk1DYGAgLQrDkES8pnZydWNWXJurra3FggULsGrVKkGpOWWys7Ph4+ODli1b8tqMoUrNbd26Ve+Y6/u+KYqCvb093N3d0b59e7364Bva/q6VCzkPHToUlZWVEIvFDEXIDGSnFQHx8uVLhIWFIS4uDh9//DFWrlwpf1hahqHZyelCXzt5fn4+AgICcPr0aYwePVpQa3PqkEgksLGxwe7duzFq1Ciuw1HJgwcPIBaLce3aNUbVnDKBgYEwNTXFV199xXhffCUlJQUikQhZWVnyQs4vX76EhYWF0VWHIAmPJa5duwaRSIQnT57Iy5AoP+sCANHR0WjdurVeu5MbIrrayaVSKc6cOQN/f3/U1dVhwYIFWL16taDVnDLu7u6YN28eevfuzXUoryCRSJCYmIgjR46gXbt2sLKywrZt21hToHfv3kV8fLxRVodQVnO2trbytTmpVIoffvgBe/bsQevWrTmOlF1IwmOQ0tJShIeHy9XcqlWrXlNzijx48AD+/v6033XxeYpLE3Sxk+fn5yM4OBi///67Qak5ZU6dOoXi4mK5nZwP09eZmZnw9fXFtWvXMH36dAQGBmpc1UNXlM/xiooKLF++HEeOHDGomxtFVP2uU1JS4OPjg+zsbLmaU16b27VrFyZOnIgBAwawFSqtkK3FeARFUfK1uSdPnuDHH3+sV80pUlNTg6VLl0IkEgnGdMAWmtrJFdVcbW0t5s2bBycnJ4O94D158gS7du16ZRsorhJeTU0Njh49ypmaU2bFihVwdnbGe++9x0n/bKJNIedLly7h1q1bCAkJYTlKfkASHk0oqrkBAwZg9erV+OCDDzR+v7OzM5YuXarx7uTGQkpKCn777Te11SGePXuGwMBAJCcnY/To0fD09MS7774LAAab7Orq6mBtbQ1vb+9X7uDZTjBcqLmGCAsLwzvvvINx48ZxGgfT3LhxA76+vvLN4lWpOUWKi4uxfv16xMfHC37WR1dIwtMDiqJw7do1iMViPH36VO3anDqOHj2Kurq6BncnNzbU2cmlUil+//13+Pv7QyqV4qeffnplbc7QK0Rs3boVs2bN4qSIr0zNhYSEoH379pyrOUXu37+P0NBQg60Ooajm+vTpA1tbW42mJmWP83h4eMDExISFSPkJSXg6UFpairCwMMTHx+uk5hTRZHdyY6Q+O/mzZ88QEBCA3377DWZmZvjll1/QqVMnDiNln3PnzuHRo0dwc3N77d+YnNLMzMyEWCzGP//8gxkzZiAoKIhzNadIVVUVli1bhoCAAIPZZEHGjRs3IBKJ8PjxY3npL23GuG/fPnzxxRcYMmQIg1HyH8M6KxhEWc1pujanDpmdXNXu5MaOop1clZpbs2aNwU5XqiM/Px+bNm2q19hEt8qqqamROy1lam779u28UHPKODs7w9HRkZebeuuC8trc8uXLX1H0ms5iXLt2DX/++SciIyOZClUwkITXAHSqOWVkdnLF3ckJ/7OTHzp0CDt27DBqNaeIrDoEG3byjIwM+Pr64vr165g+fTrv1Jwy8fHxaNasGSZPnsx1KHqjSs3pull8SUkJnJycEBMTw8ubFLYhCU8FMjUnEonw7NkzWtScMop2csL/KCsrg6WlJbp164aVK1catZpThmk7uZDUnCKy8kFCft5OVsg5NjYWH3744WtqThdkj/Ns2bIF7dq1oylSYUMSngKlpaUIDQ1FfHw8Bg4ciDVr1tCm5hRRZSdnEj48m9UQT58+RWBgILy9vTF+/Hhs27YNHTt21Lk9IYxZGzS1k+uSnDIyMiAWi3H9+nXMmDEDwcHBgjE21NTUwMbGBt7e3oJ8nEexkLO2aq6hc1wkEmHAgAEYMWIEHaHyBrK1mB5QFIWrV69CLBbL1dyvv/7K2JpafXZyY0QqleK3336Dv78/AKBHjx5YsGCB3tUhDA0m7OQ1NTVISEhAaGgo3nnnHVhZWWHHjh28V3PKuLi4wNraGj179uQ6FI2RqbmYmBh89NFHjBRyTk1NxcmTJxEbG0tru0LHaBNeSUmJfG1u4MCBcHJywvvvv894v1zayfnC06dPERAQgN9//x1jxozB7t27UVZWBkdHR4O1k+sK3XZymZq7ceOG4NScMklJSaiursbMmTMhkUi4DqdBFNWc4mbxdFNWVoYVK1YgPDycVIdQwigTnr29PV68eMG4mlNGnZ2cSfhw166s5n766SesXbsWjRs3RlVVFebNm0ernZwPY6YDbe3kUqn0tdcMRc0pkpOTg71798qXBfg6FuXSX3SqufrGvHz5cri5uck3XzA0yNZiWuLo6IhPP/2U1T4LCgqwefNmo1MwqtSc8tqck5OTQdnJ6UIXO7nixcCQ1JwitbW1sLa2xoEDBxhRSHSgWPprzpw5jKk5ZYKCgtCjRw/eVs3gGqNMeGzvKi+zk+/evdsodieXSqVITk5GQEAAAGDhwoVyNadMXFycwdjJ6URXOzlFUZBIJJg9ezY6duwIa2trwas5ZTZs2ABLS0tGDGX6oKzmVqxYQfvanDrS0tIQGxsraLcq0xhlwmMbT09PTJgwQbC7k2vK06dP4e/vjzNnzmDs2LEq1ZwiDx8+hEgkMrqaXA2hi538/v37OHjwIMrLy9G0aVOIxWKDfGYxOTkZ+fn52LJlC9ehyKmvkDObVFZWwt7eHiEhIeQRHjWQhMcwly5dQmpqqsHuTq6o5ho1aoSffvoJzs7ODS6Wy6pDHDp0CM2aNWMpWmGgqZ28urpavjbXoUMHWFpawt/fH40aNTKIqUtlnj59ip07d/LiBkmxkHP//v1VFnJmkxUrVsDJyUmvR3mEQkFBgc7vJQmPQQx5d/InT54gICBArub27NmjVSkWV1dXWFlZCcpOzgaa2Mnv378PsViMlJQUfPvttwgJCYGJiQnKy8sN7jyTIXucZ9++fXjjjTc4i0O5kDMXak6ZiIgItGvXDuPHj+c0DiZRLP1VUVGhczsk4TGEIe5OLlNzMhWxcOFCjdScMseOHUNVVRVmzpzJUKTCRPZoRkRExGufqbKas7Kyws6dO19LcIb2wL2M7du349tvv623zhuTKKo5TQo5s0lGRgaCg4N5oXqZQFb66/Tp0zAzM8OuXbvQsmVLvP322zq1RxIeQ3h7e/Nmd3J9L4JPnjyRr82NGzcOe/fu1bmwZk5ODvbs2cP4LjNCvPCrspPfv38fIpEIN2/exLfffosjR47gzTffrLcNQ3zu6sKFC8jIyICrq2u9x9D9fSsXcta19BeTVFVVwd7eHv7+/gZVHUJxs/i6urrXSn8VFRXp3LbhfEo84tq1a7h48aKgdyeXSqU4ffo0AgIC0LhxYyxcuBDr1q3T64JaW1uLJUuW8NpOzhVBQUHo3r07Ro8ejerqasTHxyMsLAzvvfcerKys4OHhYbDTleooKCjAxo0bkZCQwMr4FQs5803NKbNu3TosW7YMXbt25ToUWpCV/kpOToaZmRk8PT3RuXNnWvsQRMJ79OgRNm/ejDNnzuDp06fo1KkTLC0t4erqyjvDg9B3J8/Ly0NAQADOnj2rt5pTZsOGDfjxxx95ZyfnmrS0NMTExMDDwwNr1qzBzZs38d133zWo5gwdqVQKGxsb/PLLL2jTpg1j/ShuFk9X6S+mSUhIQJMmTTBlyhSuQ9ELVWqOyc3iBZHw7t27B6lUCh8fH5iamuL27duwsrJCeXk5PD09uQ5PDkVRsLW15d3u5A0l3rq6OrnTki41pwzbdnKh3Gy8ePEC5ubm6NSpE3bv3q23mhPiVG59eHl5Ydy4cRg4cGCDx+ryeSmX/mJqs3i6ycrKwqFDhwRthpNtFp+cnIwxY8ZoVfpLrzFTAsXDw4Pq2bOnVu8pKSmhAFAlJSWMxOTj40Pt2LGDkbb1QSKRUBKJ5LXXc3NzqS1btlBjx46lduzYQT19+pSR/p88eUKNGTOGKi8vZ6R9VdQ3Zr6Qnp5OrV69murSpQtlb29PyzlZVlZGmZiYUCYmJlRZWRkNUXLHX3/9Rc2ZM4eSSqUaHa/p9y2VSqkrV65QVlZW1NSpU6nw8HCqqqpK33BZo6amhpo4cSKVmZnJ+3Ncmbq6Our06dPU999/T5mbm1MnTpygamtrtW6nqKhI5+u4IBSeKkpKShpUUdXV1aiurpb/f2lpKYD/VBqXSCQN3ilQCnfL6o6lKAqpqak4duwYoqOj1VYi1rRNxWP1jVMxntraWiQnJyMoKAhNmzbFggULsGbNGrmakx2rS5yqjq2rq4OVlRW8vLzQrFkz+Sa/dH329R2r6juga0z1HdvQcVVVVUhISEB4eDg6duyI7t27Y86cOdi2bdtrMWtz7smora2VT4HW1dW99hlwce7pcmxxcTHWrVuHqKgo1NXVadRmQ8fJ1uYSExPx8ccfw9HR8RU1p8tnr82xdLXp4uKC+fPno1u3bq/8Vrn4njQ9Tqbmzpw5g9GjR8PDw0Ou5iiKqvc8ra9NTSu9q0KQCS8zMxPe3t745Zdf1B63fft2bNy4kfF4ysrKsHr1ahw5coS3Lrm8vDwcOXIE58+f1+m5OV3ZuXMnpk2bho8++ojxvvjKv//+C19fX9y+fVu+p2VBQQEcHR1p3waKEviUJkVRsLOzw7Zt2/SusE79d23O19cX+fn5sLCwQFxcnGANUydPnkRZWRlmzZrFdSgNIlubCwwMBEVRmDdvntxpyek0rNaakEbc3d0pAGr/rl69+sp7cnNzKVNTU2rRokUNtl9VVUWVlJTI/x4/fszIlOZPP/1EnT17ltY26aC2tpY6fvw4NWvWLMrCwoJKTk6m6urqWOv//Pnz1Lx58zSelqITrqd7qqqqqLCwMGrKlCmUlZUVdfXqVfnnUFVVRX399ddUVlYWrX0awpSmt7c35eXlpfX7FL/vkpIS6uDBg9TXX39NrVmzhkpPT6c7TNbJycmhxo0bR1VWVspf4/ocV8WTJ0+obdu2UWPGjKG2bNlC5eXl0d6HYKc07ezsYGFhofaYHj16yP87Ly8PZmZmGD58OEQiUYPtN2/enHGnlaKdnC/k5eXB398f586dw9dff409e/agQ4cOrD6rU1BQgA0bNiAxMVGwC+u6kJ6eDrFYjFu3buG7775DaGjoa05LJycn2NnZoVu3bhxFyU+uX7+O8+fPIyoqSuv3Uv8t5BwQEMBKIWc2kT3Os3//fl6qU3Wlv/gGpwmvffv2aN++vUbH5ubmwszMDIMHD5a7CblGZidPSEjgOhTU1dXJn5v7v//7PyxatAguLi5o3LixXnPeuiCzk3t5eTFqJ+cL1dXViIuLQ1hYmLxCQX3u4YSEBDRu3BjTpk1jJBZKoFOapaWlWL16NaKjo7W6QZIVco6Li8Mnn3wiGKelNmzevBkWFha8ex5Qk9JffEMQa3h5eXkYPXo0unXrBk9Pz1c2D2VjHUoVst3Jg4ODOd2dPDc3F/7+/jh//jzGjx8Pb29vdOjQgbN4AO3s5EImPT0dIpEIt2/fxnfffYewsDC1CV5mJ2dylxkhqmnqv+t2mzZt0mjLKJmaE4vFcjWXkJCA5s2bG9SOIwBw5swZ5ObmsuJF0AQhqTlVCOLsOH36NDIyMpCRkfFakVCu7mhlu5NzUYKlrq4Op06dQmBgIJo2bYqFCxfC1dW13pOOzc/o8uXLuH79OkJDQ1nrUxVMjbmqqgpxcXEIDw9Hp06dYG1tjcGDBzf4PolEAhsbG8arQwgx4fn5+aFfv34YOXKk2uNkai4hIQEDBw6Ek5MT3n//fQD/+XyFqm7r49mzZ9i6dWu9+2SyOV5Z6a/ff/9do9JfTKLPuAWR8BYsWIAFCxZwHYYcrnYnV1Zz+/fvf2XfRa55/vw5XFxcEBcXJ8gLrzru3bsHsViM27dvY+bMmQ2qOWXWr1+PhQsXolevXgxGKTxu376NpKQkxMXFqfx3iqJw5coViMVi5Ofnw9LSkve7oNCBrGj03r170apVK85iUC7krMtm8XSjzxKSIBIen2B7d3KZmgsICEDTpk2xaNEitWqOKyiKwtKlS7Fz50697eR8QVc1p8yJEydQVlYGc3NzBqIULuXl5XBwcEBYWNhr53NJSQlCQ0ORkJCATz/9FGvXrpWrOWNg586dmDJlCvr3789638qlv/i0NvfgwQOEh4fr/H6S8LSguroay5Ytg5+fH+NrBbm5ufDz88OFCxcwYcIEHDhwQGc1x4baOnDgAD777DMMHTqU8b40QZ8xy9TcnTt3NFqbU0dubi68vLwYrw4hQ0jTeg4ODnB1dZWvOSuquYKCAvz4449ISkrSaArYkGYULl68iLS0NDg7O6s9js4x61rImU1kRaM9PT3x6aef6tQGSXha4OTkBHt7e8Z2J6+rq8PJkycRGBiIZs2aYdGiRVi/fj2vTjpV6GMn5wsyNRcWFoYuXbrAyspKJzWnCN/t5FwSEhKCzp07Y8yYMa+pOWdnZ5iamnIdIicUFRXBzc2NteoQ+hZyZhNnZ2csXbpUr8d5SMLTENnu5FOnTqW97ZycHPj7+9Oi5thGVzs5X7h37x5EIhHu3r2LmTNnIjw8nLZHKbiwkwtB4aWnpyMyMhIuLi5YtGgRCgsLYWlpqbGaM1So/xaN9vT0ZLRKBl2FnNnk6NGjqKurw4wZM1BcXKxzOyThaQATdnKhqjlFtLWT84WqqirExsYiPDwcXbp0gbW1NQYNGkRrH1zZyfl+0/Hs2TNMnz4d7777Lo4ePYp169YZrZpTZs+ePRg1ahTt56IMWekvOgo5s0l2djb2799Py/WXJLwGoNtOrqzmDh48iHfeeYeGSNlHUzs5X0hLS4NYLJaruYiICLRu3Zr2fhqykxsbFEXh77//hlgsxpkzZ2BhYYGNGzcatZpT5sqVK/j777/1MmSogolCzmwikUiwZMkSHDx4kBZnLkl4DUCHnVxRzTVv3hyLFi3Czz//zPu7cXU0ZCfnC4pqrmvXrrCysmLsDhrg3k7OpynNFy9eIDQ0FImJiRg0aBAGDhyI9u3bY/v27VyHxitevHgBZ2dnxMbG0nZNYLKQM5u4ublh/vz5tM0CkISnBn3t5Dk5OfDz88Mff/yBiRMnClrNKaLOTs4X0tLS4Ovri/T0dMyaNYsxNacMl3ZygPspTUU1p7g2l5OTA1tbW6J6laAoCsuWLcO2bdvQtm1bvdpio5Azm5w6dQrPnz9vcL9lbSAJrx50tZPX1dXhxIkTCAwMRIsWLbBo0SK4ublxfiGiE2U7OV+oqqpCTEwMIiIi0LlzZyxatAjDhg1jrX9N7eSGyIsXL3DkyBEcPXoUgwcPhouLC3r37g3gf3ZykUiEpk2bchwpvzh8+DAGDRqEzz//XOc2lDeL37dvH+9+m9qSl5cHDw8PJCUl0douSXgq0MVO/vjxY/j7+8vV3KFDh3ij5uic5lK0k/OFu3fvQiwWIy0tTa7m2N6Jg207eX2w2TdFUbh8+TLEYjGKioowd+5clU5LmZ28e/fujMYiNFJSUvDbb78hOjpa6/fKbqxlhZwVN4sXOnV1dbC2tsb+/fvRsmXL1/7d4LcWYxtN7eTKam7x4sUGp+YUkdnJExMTuQ4FlZWV8rW5bt26wdra+pWHUWWV1dmALTs5X1BWc66urnI1p4yinZzwP16+fIlVq1YhMjJSqySlqObGjBmDPXv2vLa/sNDZsmULzM3N0a9fP9rbJglPCU3s5I8fP4afnx8uXryISZMm8UrNqYKOBFxZWQk7OzsEBgZyWh3i7t27EIlEuHfvHszNzREZGalybY7Nm47du3czaifXBqaUjqKaKy4u1ui5OTrt5A0hpJtM2eM87u7uGpVHUy79tXDhQri4uEAqlbIQLbucPXsWjx49gru7e73H6PNdk4SngDo7eW1trXwKoWXLlli0aBHc3d0F9UPTh9WrV2PlypXo3Lkz631XVlbK1+a6d+8OKysrnbcWopsrV67gypUrtNvJ+YJMzSUmJmLIkCFq1Zwissd56LKTGxIBAQF4//338dVXX6k9TnltTrn0l6ElvPz8fGzevJlRYxNJeP+lPju5spo7fPiwxkVrDYXo6Gi0bt0akyZNYrVfmZqTOS3rU3NcwYSdXF/oUHiKau758+ewtLTEsWPHtHpuzt3dHfPmzSMPlStx584dJCQkID4+XuW/qyvkbMjIrr979uxh9DdOEt5/UbSTG7uaU+TBgwfw9/dnzU6urOasra15WUhWVh2CDjs5nehzjj5//ly+Njd06FCsX79ep+dPT506heLiYlrt5IZARUUFli9fjtDQ0NeWBfhYyJlNdu3ahYkTJ2LAgAGM9kMSHv5nJ//xxx+xYcMGo1ZzirBpJ79z5w7EYjFv1Zwyhw4dwuDBg/Wyk/MBiqLw119/ydXc3Llzcfz4cZ2/7ydPnmDXrl2sVYcQEo6Ojli3bp38AXBtCzkbKpcuXcKtW7cQEhLCeF9Gn/CePXuGZcuWoWfPnli/fr1RqzllmLaTC0XNKZOSkoLff/9dJzs502g6pams5n7++We9i9PK7OTe3t4q7eTGTGhoKN59912MGzeO94Wc2aS4uBjr169HfHw8K9dco0142dnZ8PX1hY+PD3788Ue4uLgYtZpThkk7+Z07dyASifDvv//C3NwcUVFRnFV11paXL19i5cqViIqK4uWduLqLhqKae/Hihd5qTpmtW7di1qxZjNjJhcy///6L0NBQLF26FObm5rwu5Mwmssd5PDw8YGJiwkqfRpnwLC0t8dZbb+HNN9/E+vXrYW9vz3VIvIIJO3llZSWio6MRGRmJHj16wMrKShBqThGZnXzDhg2Cujl6/vw5QkJC8Ouvv2LYsGFwc3NDz549ae3j3LlzePToEdzc3GhtV+hkZmZi0qRJ6NixI+7duyeo0l9Ms2/fPnzxxRcYMmQIa30aZcLbu3cvCgoK4OXlBW9vb67DYRxtnHt028m5UnNMPI+mqZ2cS2QKj6Io/Pnnn/D19WVEzSlSUFCALVu2ICEhgfa2NYVPO60obhafmprK2J6WfBqztly7dg1//vknIiMjtX4v2WlFS5o0acI7OzlfoMNOLlNzERER6NmzJ6ytrfHJJ5/QGCX7NGQn5wtSqRQSiQTTpk3D8OHDGVFzyv0tWbIEXl5evDYZsYFy6a9Jkyahe/fucHV15To0XlFSUgInJyfExMSwfv01yoS3atUq3tnJ+YC+dvLbt29DJBLh/v37mD17NqKjowWzNqcOdXZyPkBRFC5duoRDhw6hsrISTZs2RVxcHN566y3G+/b09GTFTs5X6ivknJWVBRsbG+JWVUJWHWLr1q1o164d6/0bZcL75JNPBG8n1wZN7qJ0tZNXVlYiKioKkZGR6NWrF6ysrHih5ui8c1S2k/OF58+fIzg4GL/++is+++wzrFu3Tr67PBtVCWR28uDgYMb7agi2lYK6Qs41NTWwsbHB4cOHGS1yK8TZKZFIhE8++QTDhw/XuY379+/r/F6jTHh2dnZch8ArdLGTy9RcRkYGzM3NDUbNKaNoJ+cDimtzpaWlmDt3Lk6cOIGmTZuivLyctXWd4uJi/Pzzz6zZyfmApoWcXVxcYG1tzehUshBJTU3FqVOnEBMTo/V7FQs562MYM8qEZ8xWYFVoaievqKiQOy35pOaY4t9//0VYWBgvqkMUFxcjJCQESUlJ+Oyzz+Du7q7ygspG8pHtMuPh4WEU1SG0KeSclJSE6upqzJw5k+Uo+U1ZWRlWrFiBiIgIra6/aWlpEIvFuHv3rrz0V01NDYKCgnSKwygTHuF/aGInNxY1p0hVVRVsbW3lexpygSo1x5TTUhtkdvLBgwdzGgeT6FLIOScnB3v37iXrdipYvnw53NzcNKoqo6jmunbtCisrq1cqkRQXF+scB0l4RkxBQQE2b96sUsEoqrnevXvDysrKqIwJa9asgaOjIye1xpTV3IYNG9CjRw+N3sv0lOa1a9dw6dIlREREMNoPV+hayLm2thbW1tY4cOCAxkWjjYWgoCD06NEDo0aNUntcWloaRCLRK4Wc6Xb+koRnpMjs5Lt3737lpLp16xZEIhEyMzMxe/ZsxMTE4I033uAwUvaJjY1F8+bNMXnyZNb6pCgKFy9ehK+vL16+fIl58+bppOaYnNLk0k7OJLqoOWU2bNgAS0tLfPDBBwxGKjzS0tIQGxtb7+M8VVVV8u0FVak5uiEJz0jx9PTEhAkTMGDAAFRUVCAqKgpRUVFGqeYUefjwIUQiEWvTUsXFxQgODkZSUhKGDx+OjRs3aqzm2IRrOzkTKKo5fQo5JycnIz8/H1u2bGEgSuFSWVkJe3t7hISEvPY4z927dyEWixlVc6ogCc8IuXTpElJTU+Hk5AR7e3ujVnOKsGUnV6XmZE5LvkKHnZwPKJb+atGiBRYvXqy1mlPk6dOn2LFjB1m3U8GKFSvg5OSEjh07AvhPApStzXFVyJkkPCNAcV0nJycHixYtQufOnSEWi2FtbY2PP/6Yw+iYQZe1LKbt5GyoOSamGvWxk7NFQ9+3ciFnXdWcIrLHefbt28fJjSKftxaLiIhAu3btMH78eHkh53v37sHc3Fzv0l9kazFCg9y6dQt+fn6Ii4uDtbU11q5da9RqThmm7OTKam7+/Pk4efIkZ85PbdHVTs4HmC7kvH37dsyYMQMfffQRLe0ZChkZGQgICMCcOXMwefJkztScKoTxqyPoREVFBSIjIxEZGQlTU1O0bt0azs7OcHBw4Do0XsGEnbyoqAjBwcE4duwYhg8fjk2bNjFWV5BJtLGT8wVlNcdEIecLFy4gIyOD7JOpREpKCqZPn46ePXuirq6Od4WcScIzQFJTUyESifDw4UPMnj0bUVFRuHv3Lry8vLBjxw6uw2MFTe/i6bSTUxSFP/74A76+vigvL8e8efNYV3NSqZS2tjS1k/MB2S4oISEheOONN7B48WLGCjkXFBRg48aNSEhI4NStyhenrGIh58ePH2PFihVwdHRkrD99xk0SnoFQXl4ud1q+//77WLJkiXxtrqioCOvWrSPVIVRAh51cUc2NGDECmzdv5kzN0fX9NmQn5wuPHz+Gr68vLl68iIkTJ8LHx4fRWoVSqRQ2Njb45Zdf0KZNG8b6EQJ37tyBWCxGeno6Zs2aBUtLS1y9epXRZKcvJOEJHJmae/DgAb7//nvExsa+sjYnK1q6ceNGg7GT04U+dnI+qDmmUGcn5wO1tbU4fvw4goKC0KpVK3mFgkaNGjH++Xt5eWHcuHGCK15MF4pqrnv37rC2tsbAgQORlZUFa2tr3rtVhf/rNEKU1ZyNjQ369++v8liRSIQBAwZgxIgRLEfJb3S1k8vU3PHjxzlXc6qgw7mnbCfnC9nZ2fDz88Off/6Jb7755hU1V1tby3j/ly9fxvXr1xEaGsp4X3xDXSFnWdHoQ4cOMfo4Dx2QhCcgbt68CZFIhEePHqlUc8qkpqbi5MmTOlUVNmS0tZNTFIULFy7A19cXFRUVmD9/Pk6cOMFLNafvlKainZwPqFJzGzZsYH1q/vnz53BxcUFcXJzRLAvICjlHRkaiR48esLKyUqls169fj4ULF6JXr17sB6kl/PvFEl6hvLwckZGRiI6OxgcffIClS5fWq+YUKSsrg6OjoyDt5EyjqZ28qKgIQUFBOH78OL744gts3boV3bp1YylK9snIyEBwcDCOHj3KdShq1RzbyKpD7Ny5k5WiulyjTs0pc+LECZSVlcHc3JzlKHWDJDyeoq2aU0ZmJ3/33XdZme4RCg3ZyVWpOSGtzek6pVldXY1ly5bBz8+Ps7Eqq7nFixdzouaUOXDgAD777DMMHTqU0ziYRKbmIiIi0LNnT1hbWzdY+is3NxdeXl68X7dTRBi/YiNBVzWnTFBQELp3747Ro0cD4PeODEyhaszq7OSFhYXytTkhqzld1bxsm7muXbvSHFHDZGdnw9fXF5cuXcLkyZMhEonw9ttva9UGU+f49evXcf78eURFRTHSvj7QMWZZ6a/79+9j9uzZGpf+qq2txZIlS7B//37Wq0OQnVYEjrKai4uL07jyuDJpaWmIiYlBQkICvUEKHFV2ckU1V1lZKTg1RxcJCQlo0qQJpk6dylqftbW1OHbsGIKDg+VqbuPGjZyrOUVKS0uxevVqREdH8youfamsrERUVBQiIyM1VnPKbN68GRYWFujTpw9DUTKDcf2yeYSymlu2bJneWxRVVlbCzs6Ot3ZyLlG0kxcWFiIoKAgnTpzAyJEjBavm6CArKwuHDh1ibVoqKysLfn5+eqk5NpA9zrNp0yZexqcLdBVyPnPmDHJzc7Fx40YGomQWkvBY5ubNm/Dx8UFWVhYsLCz0UnPKyOzknTp1euV1Q7o71RTFMcvs5FZWVpg7d65czTk4OBicmtNmuoctO7lMzQUFBaF169aMqDm6z3E/Pz/069cPI0eOpLVdOtFkzIqFnHv16gUrKyut1Zwiz549w9atWzk1NpGdVnhOWVmZXM317dsXtra2tG84GxERgbZt22LChAm0tit0MjIyYGlpic6dO+P8+fNGreaUYdpOnpWVBV9fX/z111+YPHkyxGKxINTS7du3kZSUhLi4OK5D0Rm61JwisqLRe/fu1bstriAJj0FSUlIgEonkai4+Pp42NadIRkYGgoKCeGEn5wMUReH8+fPyLaccHR0NUs3pA1N28traWiQlJSE4OBht2rTB4sWLsWnTJsHMMpSXl8PBwQFhYWGCe5xHWc1ZW1vTWsh5586dmDJlik5GOr5ArgA0I1NzMTEx6NOnDyNqThGZndzX15fXBUTZQHFtbsSIEejbty+GDRuGFStWcB0aa2gypcmEnVxRzU2ZMkUwak4ZBwcHuLq6okOHDlyHojG3bt2CSCSSF3KmQ80pc/HiRaSlpcHZ2ZnWdtmGJDyaUFZzdK7NqcPJyQl2dnZGO01HURTOnTsHPz8/VFVVYcGCBXBwcMD169fh4eGB6OhorkNklYaUFJ12colEIndaClHNKRMSEoLOnTtjzJgxXIfSIBUVFQgPD0dMTAxMTU1hZWVFq5pTpKioCG5ubpxXh6ADkvD0QHltzs7ODh9++CFr/SckJKBx48aYNm0aa33yhcLCQgQGBuLkyZP48ssvsX37dvkzZKWlpVi7di0iIiIE/wOlGzrs5I8ePYKfn59czfn6+gp+Y/L09HRERkYiMTGR61DUoqjmZs6cicjISLz55puM9UdRFGxsbODp6cloP2xBEp4O3LhxAyKRCNnZ2ZgzZw5ja3PqyMrKwsGDB5GUlMRqv1yiSs05Ojq+sjYns5O7u7sLckpNX9RNaepjJ1dWc1ZWVoJWc4rIHucJDAzk5eM8FRUV8ufmTE1NYW1tjY8//piVHZT27NmDUaNGYdCgQYz3xQaCSXjTpk1DSkoK8vPz0bZtW4wbNw47d+58zYLPFGVlZYiIiEBMTAz69esHe3t7VtWcIhKJBEuWLBHE7uR0UFBQgKCgIJVqThkh2MmZpL4EpKud/NGjR/D19cXff/9tMGpOmdWrV2PlypXo3Lkz16G8wq1bt+Dj41Nv6S+muXLlCv7++2+Eh4ez1ifTCCbhmZmZwcXFBR07dkRubi5Wr16NWbNm4dKlS4z2K1Nzjx8/ZtRpqQ0yO3nv3r01Ol6IW4spqrnq6mrMnz8fK1asUHsHrmgnr6urYzFa/qAq4WlrJ5dIJHKnpYmJCRYvXozNmzfzWs3peo5HR0ejdevWmDRpEs0R6UZFRQUiIyMRFRUFU1PTVwo5K8Pk7/rFixdwdnbmZdFovcZNCZTExESqUaNGVE1NjcbvKSkpoQBQJSUlao97+fIlJRaLqQkTJlCOjo7UnTt39A2XNo4fP04tXbpUq/fU1NRo9TlxSX5+PrVr1y5q7Nix1IYNG6js7GyN3ldWVkaNGTOGevr0KUVRwhozXZSVlVFvvfUW9dZbb1FlZWXy17dt20aJxeIG3//w4UPK1dWVGjduHLVnzx6qqKiIyXBpRZfvOzMzk5o4cSIvzpObN29Stra21DfffEMFBgZS5eXlDb6HqXNcKpVSc+bMof766y/a26aDwsJCja7jqhCMwlOkuLgYoaGhGDFihForfnV1Naqrq+X/X1JSIn+/RCJ57c7l5s2bCA4ORm5uLr777jv4+fnJnWzFxcX19kMp3HE0dDeky7Gy4/Ly8rBjxw6EhYW9Ek9DbUokEgBA06ZNNe6frTHJXrt48SKOHDmCmpoaWFhYICwsTK7m1H32svc7ODjAzs4OTZs2lX+/AF45P9gcE11tNnSs4nEVFRVo3bo1gP/Ub6uursZff/2FlJQUHDx4EEVFRa+1KZFIcOrUKURGRqJNmzaYO3eu/DEOiqI0+uyZHJOmbcrWs9RdDxS/p5qaGixevBheXl54+fKl3v03dKyq48rLy5GQkIDExET06tULc+fOxUcffQSKolBZWYnKykq1bcrO8f/7v/+j9dzz8/NDnz598P777/PiuqfM8+fPX2tTY3TJsFzh5OREvfHGGxQA6vPPP6cKCwvVHu/u7k4BIH/kj/yRP/JnYH+ZmZla55BGFMXdAs+GDRsadIxdvXoVQ4YMAfAfK3pxcTGysrKwceNGmJiYICkpqd47AWWF9+LFC3Tv3h3Z2dkwMTGhbyA8p7S0FF27dsXjx48NwlqsCcY4ZoCM25jGbYxjBv4zU9etWzc8f/5c64K8nCa8wsJCFBYWqj2mR48eKh+QzcnJQdeuXXHp0iUMHz5co/5KS0thYmKCkpISozpBjHHcxjhmgIzbmMZtjGMG9Bs3p2t47du3R/v27XV6ryxPKyo4AoFAIBDqQxCmlStXruDKlSsYOXIk2rZtiwcPHsDNzQ29e/fWWN0RCAQCwbgRxHbgLVu2RFxcHMaOHYs+ffpg4cKF6N+/P86fP4/mzZtr3E7z5s3h7u6u1XsMAWMctzGOGSDjNqZxG+OYAf3GzekaHoFAIBAIbCEIhUcgEAgEgr6QhEcgEAgEo4AkPAKBQCAYBSThEQgEAsEoIAmPQCAQCEaB0Sa8adOmoVu3bmjRogU6duyIuXPnIi8vj+uwGOXRo0dYtGgRevbsiZYtW6J3795wd3dHTU0N16ExztatWzFixAi88cYbWm9HJBQOHjyInj17okWLFhg8eDD++OMPrkNinAsXLmDq1Kno1KkTGjVqhISEBK5DYpzt27dj6NChaNOmDd59913MmDED6enpXIfFKIcOHcKAAQPw5ptv4s0338Tw4cNx4sQJrdsx2oRnZmaGqKgopKenIzY2FpmZmZg1axbXYTHKvXv3IJVK4ePjgzt37mD37t04fPgwXFxcuA6NcWpqamBubo6lS5dyHQojREZGwtHREa6urrhx4wa+/PJLTJo0CdnZ2VyHxijl5eX45JNPsH//fq5DYY3z58/D1tYWly9fRnJyMmprazF+/HiUl5dzHRpjdOnSBTt27MC1a9dw7do1jBkzBtOnT8edO3e0a0jr7aYNFF3q6xkCHh4eVM+ePbkOgzUCAgIoExMTrsOgnWHDhlE2NjavvNa3b1/K2dmZo4jYBwAVHx/PdRisk5+fTwGgzp8/z3UorNK2bVvK19dXq/cYrcJTRNP6eoZISUkJ2rVrx3UYBD2oqanBP//8g/Hjx7/y+vjx43Hp0iWOoiKwhazOp7H8juvq6hAREYHy8nKtt5Y06oS3du1atGrVCm+//Tays7ORmJjIdUiskpmZCW9vb9jY2HAdCkEPCgsLUVdXhw4dOrzyeocOHfD06VOOoiKwAUVRWLlyJUaOHIn+/ftzHQ6j3Lp1C61bt0bz5s1hY2OD+Ph4fPjhh1q1YVAJb8OGDWjUqJHav2vXrsmPX7NmDW7cuIHTp0+jSZMmmDdvnm5VdDlG23ED/6mePnHiRJibm2Px4sUcRa4fuozbkFGuC0lRVIPVpQnCxs7ODqmpqQgPD+c6FMbp06cPUlJScPnyZSxduhTz58/H3bt3tWpDENUSNMXOzg4WFhZqj+nRo4f8v2XliT744AP069cPXbt2xeXLlwVXgUHbcefl5cHMzAzDhw+HSCRiODrm0Hbchkr79u3RpEmT19Rcfn7+a6qPYDjY29vj6NGjuHDhArp06cJ1OIzTrFkzmJqaAgCGDBmCq1evYu/evfDx8dG4DYNKeMZaX0+bcefm5sLMzAyDBw9GQEAAGjcWrsjX5/s2JJo1a4bBgwcjOTkZ3377rfz15ORkTJ8+ncPICExAURTs7e0RHx+Pc+fOoWfPnlyHxAkURWl9vTaohKcpxlpfLy8vD6NHj0a3bt3g6emJgoIC+b+99957HEbGPNnZ2SguLkZ2djbq6uqQkpICADA1NUXr1q25DY4GVq5ciblz52LIkCFy5Z6dnW3w67NlZWXIyMiQ///Dhw+RkpKCdu3aoVu3bhxGxhy2trYICwtDYmIi2rRpI1f2JiYmaNmyJcfRMYOLiwsmTZqErl274uXLl4iIiMC5c+dw8uRJ7Rqi3SsqAFJTUykzMzOqXbt2VPPmzakePXpQNjY2VE5ODtehMUpAQAAFQOWfoTN//nyV4z579izXodHGgQMHqO7du1PNmjWjBg0aZBQ29bNnz6r8XufPn891aIxR3284ICCA69AYY+HChfJz+5133qHGjh1LnT59Wut2SD08AoFAIBgFwl3AIRAIBAJBC0jCIxAIBIJRQBIegUAgEIwCkvAIBAKBYBSQhEcgEAgEo4AkPAKBQCAYBSThEQgEAsEoIAmPQCAQCEYBSXgEAoFAMApIwiMQBEp4eDhatGiB3Nxc+WuLFy/GgAED5EVBCQTC/yBbixEIAoWiKAwcOBBffvkl9u/fj40bN8LX1xeXL19G586duQ6PQOAdRlktgUAwBBo1aoStW7di1qxZ6NSpE/bu3Ys//vhDnuy+/fZbnDt3DmPHjkVMTAzH0RII3EMUHoEgcAYNGoQ7d+7g9OnTGDVqlPz1s2fPoqysDEFBQSThEQgga3gEgqA5deoU7t27h7q6uteqm5uZmaFNmzYcRUYg8A+S8AgEgXL9+nWYm5vDx8cHEyZMwM8//8x1SAQCryFreASCAHn06BEmT54MZ2dnzJ07Fx9++CGGDh2Kf/75B4MHD+Y6PAKBlxCFRyAIjOLiYkyaNAnTpk2Di4sLAGDw4MGYOnUqXF1dOY6OQOAvROERCAKjXbt2SEtLe+31xMREDqIhEIQDcWkSCAbKhAkTcP36dZSXl6Ndu3aIj4/H0KFDuQ6LQOAMkvAIBAKBYBSQNTwCgUAgGAUk4REIBALBKCAJj0AgEAhGAUl4BAKBQDAKSMIjEAgEglFAEh6BQCAQjAKS8AgEAoFgFJCERyAQCASjgCQ8AoFAIBgFJOERCAQCwSggCY9AIBAIRsH/A9q6pvg811xhAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(X_grid @ A.T, \n",
    "          X_circle @ A.T, \n",
    "          X_vec @ A.T, \n",
    "          '$A$')  # 绘制应用 A 后的图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de51b73f-5658-42df-9aeb-468c1261ed6a",
   "metadata": {},
   "source": [
    "## SVD 分解：A = U @ S @ V.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b8fdf18e-ad05-406b-841a-08207d760cd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "U, S, V_T = np.linalg.svd(A)  # SVD分解\n",
    "S = np.diag(S)  # 构造对角矩阵 S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ff48aa16-3b99-4aec-ae4a-eefd94fa4bf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 保证和纸质书结果一致\n",
    "if U[0, 0] < 0:\n",
    "    U[:, 0] = -U[:, 0]\n",
    "    V_T[0, :] = -V_T[0, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4ec0fa8-8e84-475a-898f-754d3e030f11",
   "metadata": {},
   "source": [
    "# 输出 SVD 的分解结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4b3252b2-1a21-40eb-afdc-93277df5020d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== U ===\n",
      "[[ 0.86602858 -0.4999945 ]\n",
      " [ 0.4999945   0.86602858]]\n",
      "=== S ===\n",
      "[[1.9999835 0.       ]\n",
      " [0.        0.5000165]]\n",
      "=== V.T ===\n",
      "[[ 0.86602858  0.4999945 ]\n",
      " [-0.4999945   0.86602858]]\n"
     ]
    }
   ],
   "source": [
    "print('=== U ===')  # 打印 U\n",
    "print(U)  # 显示 U\n",
    "print('=== S ===')  # 打印 S\n",
    "print(S)  # 显示 S\n",
    "print('=== V.T ===')  # 打印 V.T\n",
    "print(V_T)  # 显示 V.T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66eeeb08-1503-461e-98f2-ccee9430bbcc",
   "metadata": {},
   "source": [
    "## 绘制应用 V^T 的变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3c4669ba-afb7-4324-b5d1-4e4424c9e128",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(X_grid @ V_T.T, \n",
    "          X_circle @ V_T.T, \n",
    "          X_vec @ V_T.T, \n",
    "          '$V^T$')  # 绘制应用 V^T 后的图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d463139-23dc-4e7a-bd92-b07f3ea9ca5c",
   "metadata": {},
   "source": [
    "## 绘制应用 S @ V^T 的变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "18633f18-cae2-4570-b6fc-938e2852e775",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(X_grid @ V_T.T @ S, \n",
    "          X_circle @ V_T.T @ S, \n",
    "          X_vec @ V_T.T @ S, \n",
    "          '$SV^T$')  # 绘制应用 S @ V^T 后的图像"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4b4b9ae-81d3-4151-be3f-8fcdec76697a",
   "metadata": {},
   "source": [
    "## 绘制应用 U @ S @ V^T 的变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5621fad9-ec4d-4be1-9eb7-f075aa256882",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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y8tJ7NacMzuHRTFZWFhYvXqxSOHlERAT4fD5evnxZKtWcIrt27cLgwYPRqVMnRu2QV3OJiYk6mZsrDm3CyfXNCShTc6tXr1Y6xy1dzrNx40bUqlWLAWvZy//+9z98+vQJGzZsUPmYnJwcBAcHw9vbW6bmduzYoXf3kDpwDo9mSgonl6o5Hx8fNG3aFObm5oxXKNAFN2/exKNHj+Dp6cmYDVI1FxYWhu7duzOm5uShO5ycLaii5hQRCARo164dfvvtNx1ZqR98+fIFW7ZsUfkF6dWrV+Dz+aVezSmDc3g04uvri1q1aikNJ4+IiICTkxNevXqFiRMnws/PjzY1x7ZhrqSkJNja2iIkJIS2t8mizllRzc2cORMnTpxgjXPRNpyczW/n6qg5RZ4+fYqTJ08iKChI6Xa23eO6gBACiUQCCwsL7N+/v9hyUMrU3M6dO3VoLXVwmVZYyJs3b+Dh4YGwsDDZZ1lZWbJIy6ZNm8LCwgKdO3dmzkgGkFaH2L59u05z6yUlJcnm5nr06IE1a9bI1m6xBarDydlCXFwchEIhLl26hMGDB6uk5uTJyMjAsmXL4OPjw62zU8DBwQGjR49Gu3btlG5/9eoVnJyc8OzZM1Yni9cVnMOjgZycHCxYsEAWTv78+XPw+XydqDm2c/DgQfTu3Vsn4eSEENy4cQN8Ph9JSUmYOXMmTp48ycoUa1SGk7MBsViMM2fOwNXVFeXLl4eJiQlsbW01clhLlizBmjVr8OOPP9Jgqf5y7do1vH79utByHn0o/cUUnMOjgZUrV8LCwgKXLl1ihZpjyzCXrsLJk5KS4ObmhuPHj6Nnz55Yu3Yt69ScPFSEk0themjv48ePcHZ2xuXLlzF48GAcPHhQK0fl7u6Oxo0bo1+/fsXux5Z7XFfEx8djw4YNCA4Olp27tPTXs2fPMGHChFKr5rjUYixi3759uHr1Kl6/fo1JkybB39+/2LH1sgLd4eSEENy8eVOm5qZPn45jx46hcuXKlPdFNdqEkyvChMOjUs3J8/LlSwQEBCA0NJQaQ0sJ0uU8Dg4OKF++PLy9vTk1pyKcw6OArKwsBAQEwMXFBW/fvkVQUBCXAUIOOsPJk5KS4OHhgWPHjhVQc/qSakqTcPLi0KXSoVrNyZOVlYVFixbB3d2dqw6hwJ49e9C2bVt4e3vLksWXVjVHNZzD04Lnz5/DyckJr1+/xrhx41CuXDlcvnyZ8oSt+g7V4eTSuTmBQIDk5GRWz80Vh7rh5GxALBbj9OnTcHV1RYUKFWBqakqJmlPkn3/+wYoVK9CwYUNK29VnsrOz4eDggKNHj2LUqFEwMTFBt27ddF7FXJ/hvik1kao5X19fNGvWDBYWFujUqRNWrlwJS0tLztkpUFI4uTooqrl169bp7fetaji5utA1pPnx40cIhUJcuXIFQ4YMwaFDh2gLIvH390eNGjUwdOhQWtrXN6SFnB8/fowPHz7g1q1baNKkid6MYrAJzuGpyLNnz+Dk5ITIyEhMmjQJAQEBsgdVaQ0n1xYqwskV1dysWbP0Us0psm3btmLDyTWFyiFNZWqO7npzb9++hYuLi16pXjpQLP1lZmaGuLg4bNmyBU2aNGHaPL2Fc3jFkJWVBX9/f/j5+RVQc/KUtnByKtEmnLw0qTlFrl69ilevXsHGxoZpU5Ty4cMHODs760TNySNdzuPk5KT3LzSaUlQh50OHDqFHjx749ddfmTZRr+EcnhLk1dzkyZMLqDl5qAwnL22oGk4uj/y6udTUVL2dmyuO+Ph42NnZsa46BBNqThFra2ssWLAATZs21VmfbKCkQs4PHz7EhQsXKCkaXdbhHN53MjMzERAQAD8/PzRv3hzm5uYlJjWmMpycTnQdqq5uOHliYiI8PDxw/Phx/Prrr7Czs9NazTG9Hk0Z0iwzu3btoi2iTl0n+uHDB9nc3NChQ3H48GGN6jVqS1hYGAghGDNmjEbHs/F6l4QqhZzT0tLwzz//wN/fv9DLhz6eMxVwqcW04NmzZ3B0dMSbN2+KVXOKUB1OXlpQNZycEILr169DIBCUWjWnyJ49e9CvXz/Gk4OLxWKcOnUKrq6uqFSpEkxNTbFu3TrGFOf79+9x6NChMjEtoE4hZ+lyHnt7e9SpU0fHlpZOyqTDy8zMRHBwMPz8/NCiRQuV1Jw8+hhOritKCidXVHPr16+HsbGxbo1kgDt37uDu3bvw9vZmzAapmrt69SqGDh2KI0eOMKLm5JGvDlGxYkVGbaETTQo5Ozs74+eff8bvv/+uIyv1g2/fvml8bJl0eDNnzsT06dMRGBiodkg4XeHkdKKrN/eiwskJIbh27RoEAgHS0tJ0EmnJpvmx5ORkWFtbF0gDRRcSiaTA32xTc4qsXbsWc+fO1bosE1vORx5tCjk/e/YMx44dK7ZoNBvPmW4kEgmsrKw0Pr5MOrygoCCN6z/RFU6u7ygLJ09MTIS7uzuOHz+O3r17w97evkyoOXkIIZg/fz62bt2KmjVr0t6f9CH44cMH+Pr6skrNKXL69GmkpKRg8uTJTJtCKdJCzuqoOXkyMjKwdOlSeHt7c9UhFHBwcMCgQYNw6tQpzRogZYiUlBQCgKSkpGh0/JUrV8isWbOIRCKh2DJ6EYlERCQS0dZ+dnY2GTx4MImOjiYSiUT2PY0bN46EhISQ3Nxc2vouCrrPWVUOHTpEdu7cqZO+kpOTSZUqVUi5cuXIlClTyMWLF1l7r378+JEMGDCAZGZmUtIe09c7MzOTeHh4kOHDh5P58+eTBw8eaNyWmZkZOX/+fIn7MX3OuubatWtkxowZJD4+XuPneJlUeJrA1nByNmBtbY2ZM2ciJCSkTKs5RaTh5P7+/rT2ExsbC6FQiMuXL0MsFqNSpUoQCoWsHXIXi8WwsLDAwYMH9SK5d3FICzm/fPkSkyZN0rr0l6enJxo0aIABAwZQaKX+k5CQgLVr1yI0NFSrDDOcw1MBooNwcn2EEIJt27bhzJkziImJwaxZs3D69Gkutx+KDyengry8PJw6dQpubm6oXLkyTE1NsWLFCjRq1Ijyvqhm48aNmDx5Mtq0acO0KRqhWMjZ3Nycksjb169fw9fXl6sOoYD0+btz505IJBLw+XyN2+KeTCrAlnBytpCQkAB3d3cEBQUhLi4Op0+fZv1aRF1CaAwnl6q5a9euYdiwYTh69Kisj4yMDEr7ooMLFy4gJiYG69evZ9oUtZGqOToKOWdnZ2PhwoVwdXXlXhgV2Lt3Lxo1aoSDBw8iKSlJ47WaAOfwSoQN4eRsgBCCq1evQiAQICMjA9OnT0f16tVx7tw5rSPsShtUh5NL1ZyrqyuqVKkCU1NT2NnZKR1aJyxejPz161ds2rRJr5bzKKo5ugo5r1ixAsuXL8dPP/1Eedv6SlJSEjZv3gwPDw+YmJhg8eLFaN68ORITEzVuk3N4xaDLcHI60eYhKFVzJ06cQJ8+fbBx40Y0bdoUNjY2lIST0wVTD/5nz54hPDy82HByVYmNjYVAIMD169cxbNgwODo6lqgY2RrVJ13Os3fvXspUkTxUX29p6a9Xr17RXsg5MDAQVapUwfDhw9U6js0vN5pC5Ao5f/36Fe/fv8fjx49Rv379AvtoCufwioDoOJycTSiqOcW5uTNnziA5ObnUhZNrizSc3MvLS+OipXl5eTh58iTc3NxQtWpVmJqaYv369Xr9wgXkh5MPHz4cHTt2ZNqUIpGW/vLz84OxsTHMzc1pUXPyvHv3DkKhUK9ULx0kJSXB09MT4eHh6NGjB9asWYO1a9eCz+cXcHbawjm8Ijhy5Ai6d+9eprKTF6Xm5ImLi8OOHTvKRBoodVm2bBlsbGw0+oHGxMRAKBTi+vXrGD58uEpqTl+4fv06nj17Bg8PD6ZNUYp8IWe61Zw8ubm5mD9/PhwdHUt1Sr2ikFdzioWcjx49is6dO6N3796U9sk5PCU8evRIJ+HkuqI4dSCv5tLT0zF79uwiIy3FYjEsLS31Ipxc14rI09MT9evXx8CBA1U+hg41x7ZhLvlwcjqvibptM6HmFLGxscG8efM0Xr6jr6q/pNJfjx8/xtmzZxEYGKj0eG3Om3N4CkjDyf38/Fg7H0IFCQkJcHNzw8mTJ/Hbb78pVXOKbNq0CZMmTdLbcHK6eP36NXx8fBAWFqbS/qVZzckjDSffsWOHxpmNqIYpNafIsWPHkJeXh3Hjxum8byYgCoWci0oWn56ejuXLl9P2/OUcnhyEECxatAjr168vtQ+gK1euQCAQIDMzs1g1p8jFixfx/v172NnZ6cBS/UEaTu7i4lLs96io5szMzErF3Fxx7Nu3D7///ju6devGqB1SNefr61tkIWddEhsbiwMHDpSJaQF1CjkTQrB48WLY2dnRlgaPc3hyuLi4oHXr1qUuO3l8fDw8PDxw5swZ/Pbbb9i8eTOaNGmi8vHScHJVFUxZYsWKFVi2bFmRC75jYmIgEAhw48YNjBgxAk5OTqhduzZt9rBlSPPu3bu4desWfHx8GLNB1ULOukRaNPrw4cOltjqEoppTNVm8m5sbmjVrhj///JM22ziH953nz58jLCyMknByNiCv5jIyMjBz5kwsX75c7UWtEokElpaW2LNnDy3h5PpMYGAgKleujBEjRhT4PC8vDydOnIC7u7tMzdnb2+tEzbFBMaakpGDVqlUICgrSuT2aFHLWJXZ2dpg1axZatmzJtCmUo46aUyQiIgLBwcEICQmh1UbO4SH/R7JkyRKtwsnZQnx8PNzd3WVzc5s3b5bVptMkg8OOHTswbNgwVoeTM8G7d+8gEAgKhJO/f/8eQqFQZ2qOjRBCsGDBAmzZsgU//PCDzvp99uwZBAIB3r17h0mTJrFCzSly9uxZJCQkYOrUqUybQhmEgkLO0uevh4cH7c9fzuEBWLp0qcbh5GxAXs1lZWUVmpvTNNnqjRs38PTpU9aGkzOFfDi5gYEBwsLC4ObmhmrVqulUzSmD6SFNR0dHdO7cGb169aK9L3k1Z2xsDFNTU8bnC4vi06dPcHBwKDXr7RQLOdvZ2ams5hSxsrLCqlWr0KBBA4qtLEyZd3iahJOzhfj4eLi5ueHUqVMazc0VR0JCAtasWUN7OLk+YmNjg/Hjx0MoFOLmzZsYMWIE+Hw+K9Qck9eqpHByqnj27BkcHR3x5s0b2dwcm+fDpMt59u/fjypVqjBtjsZQoeYU8fHxQe3atTFo0CAKLS0GjQoT6SmK9fBevXpFhg8frlc1pSQSCbl48SKZMWMGmTBhAgkPDy/R/tzcXLVq0kkkEjJx4kRy7949bc1lDHXPWRVEIhGxtbUlzZs3J7NmzSJXrlxhVb259PR0UrNmTVKzZk2Snp6u077T0tJI//79ydevX2lpPyMjg7i4uJBhw4aRRYsWkcePHxfYTsf1pooNGzYQFxcXytvV1TknJCSQvXv3koEDBxJbW1sSFRVFSbuvX78mw4YNU/v5y9XD0wBVw8nZgrya69u3L6VqThG2hJOzhffv30MgEODixYv49u0brly5wiX5lYN8Dydft24d5eHkT58+hZOTE96+fYvJkyfL8k7qC5cvX8a7d++wZs0apk1RC0IIrl27BoFAgLS0NJUjLVUlJycHCxcuhFAo1Onzl/1PepqQZidnc/0wQgguX74MgUCA7OxszJ49G0uXLqX1Brl79y5u3LgBPz8/2vrQB0QikSzSsnr16pgzZw7u378PFxcXztkp4ObmhubNm1MWTp6ZmQl/f3/4+/ujRYsWMDc318ugqW/fvmHDhg16VTQ6MTER7u7utBdyXrlyJRYvXozGjRtT3nZxlEmHFxoaqlF2cl0RHx8PV1dXnDp1Cr///ju2bt2q1Y2h6o8tJSUFK1euZCScnGo0tT86Olo2Nzdy5EgIBALUqlULtra2mDlzJlq1akWxpdRCdBy0QmU4uTZqjm33q3Q5z+7du2lbzkPVOStTc6dOnaItv2dISAjKlSuHUaNGaXQ8l1pMTTw8PHDy5EmmzSgAIQSXLl2CUChEdnY25syZg2XLlulM7pPv1SG2bNmCWrVq6aRPtqCo5szNzbFhwwbZD+vs2bOIj4/HtGnTGLaUXVARTi5Vc35+fmjZsiUsLCzQoUMHii3VPbt27cLgwYNZtQZQEV2pOXmio6Ph6OjIWLRqmXR4u3fvZk128m/fvsHNzQ2nT5+mRM1pijScnOrs5GwmOjoaAoEAt2/fLqDm5Pn06RO2b9+uN2mgdKnwtAknf/r0KRwdHfHu3TtMmTIFQUFBejU3Vxw3b97Eo0eP4OnpybQphVBUc+qkF9QWkUiEefPm4ciRI6hQoQLt/SmjTDq8kpIk0w3Tak4RXYWTswGRSITjx4/D3d0dRkZGMDMzw8aNG5UOk0jDyQ8cOKA3D2NdDe1pEk6ekZEhm5tr1aoVLC0tS4WakycpKQm2trYICQlh1TCrfOmv3r17Y8OGDTp/Dtra2sLMzEzj9XpUUCYdHlOwRc3JQ3d2cragqOaEQmGJQ7dbtmzBuHHj0LZtWx1ZqR9ERkbCw8ND5WGpJ0+ewMnJqVSqOXnI9+oQ27dvh5GREdPmlFjIWZecPHkSmZmZmDhxos77lodzeDQjVXMCgQA5OTmYM2cOli9fzooUZkQH2cmZRCQS4dixYyqpOUUuX76Mt2/f6mU4OZ1kZ2djwYIFcHZ2LvbBWRbUnCIHDx5E79690aNHD0btUKWQsy758OED9uzZw4ppAb1yeFu3bkVwcDBevnyJypUro0+fPti+fTt+/vlnpk0rxNevX2Vq7o8//sD27dtZtwRCF9nJmSA6OhpOTk64c+cORo0apZKak+fbt2+wt7fXq3ByKXTbu3LlSixZsqTIkYknT57A0dERUVFRpVrNKXL//n1cvXqVseU8bFJz8kirQxw6dAiVKlVi1BZAzxze5cuXsXDhQvTo0QN5eXmwtbXF4MGDERERwYpEsYQQXLx4EUKhELm5uZgzZw6srKxYoeYU0VV2cl0hPzdXs2ZNzJkzB/b29moHJ8lXh6hevTpN1uonwcHBKF++fKFw8oyMDPj5+SEgIACtW7fG/Pnz0b59e4as1D2pqan4999/ERgYqPMXpISEBHh7e+PkyZOsUHOK2NvbY/r06WjdujXTpuSjdm4WFvH161cCgFy+fFml/RVTi1HFly9fiIODAxkwYACxt7cnsbGxlLavLYopiDIyMsiAAQNIXFwcg1ZRw7t378jq1avJwIEDyb59+0hCQgIhRPO0Sw4ODuTIkSNUm6kT6Ewt9u7dOzJ48GCSk5Mj++zRo0dkwYIFZNiwYcTNzY1kZGRQ2qc6MJVaTCKRkBkzZpBr167ptM9Lly6R6dOnk7Fjx5KwsDBWpkc8d+4cMTMzo7zdMptaLCUlBQCKHK7KyclBTk6O7O/U1FQA+WpAJBKV+DZG5OZDFPeVSCS4fPkynJ2dkZubi1mzZmHx4sUlVigors2i9tXGTnlbeDweCCFYtmwZ/vnnH9StW5dSO9XZV5s2pWrOy8sLRkZGMDExgZ2dHXg8Hng8HvLy8gqcs6p23rx5Ew8ePIC7uztEIpFOz0nTfeX3y8vLQ40aNQDkR5gqXltNr1Nubi7mzZuHgwcPIisrC25ubggKCkKrVq1gZmYmU3PS757Kc1LVTmXXu7hzUqVNVfYVCARo06YNevbsScm5F7evdG7u9OnT6NOnD+zs7NC4cWOVqqLQfe8p7vf582ds2bIFISEhyMvLo/QZoWn1F0DPhjTlIYTAysoKffv2LXL4ZOvWrbC3t6e0369fv8LDwwNnz56VRVqyPdWU/I3j6+uLWrVq6WV1iKioKDg7O+Pu3buyenO1atVSGqih7tBSUlIS1q1bJxuWUtamPkCH3WvXrkX//v2xe/duvH//XlZvrnLlyqz5npiYa3369ClOnToFf39/2vog3+fmhEIhsrKyMHPmTJw4cQLlypXT6sFPJ2KxGAsWLMCePXtomWrS6lqrrQlZwoIFC0jTpk2LHT7Mzs4mKSkpsv9iY2M1ksJisZicP3+eTJs2jUycOJEcP36c5OXlaXsKOkMkEhGRSKRxdnImyc3NJUFBQWTMmDFkzpw55Nq1aypVKJCesypIJBIyefJkcufOHW3NZZT09HRiZGREjIyMKBnSTE9PJ0uWLCFNmjQhS5YsIc+ePaPASnpQ53pTQXp6Ounfvz/58uULLe1/+/aN7Nq1iwwYMICsW7eOvH//vtA+uj5nVdm0aRMRCAS0tZ+QkFC2hjQXL16M8PBwXLlypdjIx4oVK2pVJ+vr169wdXXFmTNn8Oeff8LBwYF1kZaqwlR2ck2JiooCn8/H3bt3MXr0aLi4uNBWQZst4eRUQChQXI8fP4ajoyNevnyJL1++4NGjRzqtXq4PLFmyBGvWrMGPP/5IWZukhELO+sDVq1fx6tUrrF69mmlTlKI/3yT+WzcWEhKCS5cu0bJiXyKRyCItRSIR5s6di3/++YeVkZbqYG1tzUh2cnUQiUQIDw+Hh4cHfvjhB5ibm2Pz5s20DlcxHU5ONZp+V+np6bJIyzZt2sDS0hKrV69GSEgI5+wUcHd3R+PGjdGvXz9K2tNl6S86iY+Ph52dHauX8+iVw1u4cCG8vb0RFhaG6tWr4/PnzwAAIyMjVK5cWau25dXcX3/9hR07drB+bk5VQkNDtcpOTjfv3r2DQCDQiZqTh8lwcrbw6NEjODk54f3795g6dSpCQkJQuXJlrF27ll3h5Czh5cuXCAgIQGhoqFbtkO+lv6Rzc7oo/UUn0uU8u3btYvdyHoqHV2kFgNL/VK0mrLgsQX5ubtKkSeTEiRN6NTenClFRUWTw4MGMhowrIzc3lwQGBsrm5q5fv05p9fCS5jeYCCenm/T0dFKjRg1So0aNYufw0tLSiEAgIEOGDCFLly4tNDdHVzg5nehiPiszM5MMHDiQfPz4UeM2vn37Rnbu3EkGDBhA7OzslM7NqQqb5vB27txJDh48qJO+yswcHqEoIuzbt284cuQIzp49W+rUnDzS7OQHDx5kLDu5IkypOUUEAgHatWuH3377Ted900lxSvXRo0dwdHRETExMATUnz+fPn7F161bGyrewmX/++QcrVqxAw4YN1TqOMFDIWZfcvn0bd+/ehY+PD9OmlEjp+MbVZMWKFTA3N8eKFSv0fm6uONiQnRwoODdXq1YtnczNFcfTp09x8uRJBAUFMdK/LklPT4evry8CAwPxyy+/YPHixUUmw5ZWh9i/fz8rMhexCX9/fxgZGWHIkCEqHyMt5MymZPFUk5SUBGtra9ZVhyiKMunw3NzcZAt0Syvy2cnlF1Hrknfv3oHP5+PevXsYM2aMTtVcUaMBGRkZWLZsGXx8fEpldQjpQ+fx48fw8PBATEwMpk2bplTNKbJt2zaMHj0a7dq104WplELV6I8y3r59C1dXV4SFhalkh65Kf9F5zqr2P3/+fGzbtg01a9bUab+aUiYdXmmHyezkIpEIYWFh8PT0lKm5LVu2sObtj45wcraQnp6OnJwciEQieHt7F6vmFGF7ODlT5OTkYMGCBeDz+cXmZWVj6S+6OXz4MHr06IFff/2VaVNUhnN4pQymspO/ffsWAoFApuZcXV11+tanCm5ubpSGk7OFhw8fwsnJCdHR0eDxeKhatSq2b9+u8rCkPoSTM4W1tTUWLlyodJmAvJrLycnB7NmzWVP6i24ePnyICxcuICAggGlT1IJzeKWMDRs2FAonp+shlpubi/DwcFaqOUUbpOHkqgxL6QOKc3NLlixBkyZN1A6+0ptw8hKg456TBu6MHj26wOeKam7btm2MJKRg6neWlpaGf/75B/7+/jqfFoiOjsbBgwc1Pp5zeKWI//3vf/j06RM2bNhAaz/6oObkycrKwqJFi+Du7q73b99SNRcbG4tp06YhNDRUpuQzMjLUnt/Ys2cP+vfvjy5dutBhrt4SExODQ4cOyaYFFNUcmwo56xJCCBYuXAh7e3vUqVNHJ33Kl/4yMjLCpEmTsGvXLo3a4hxeKeHLly/YsmULbeHkUjXn4eGBOnXqsErNlYSVlZVG4eRsIT09HT4+PggMDETbtm2xZMkS/PLLL0r3Ved66FM4uS6RLuc5fPgwkpOT4ebmhjNnzuCPP/5gTM2xBWdnZ/z888/4/fffae8rOjoaAoEAt2/fxsiRI2WFnBMTEzVuk3N4pQCJRAILCwtawsnfvn0LPp+P+/fvY+zYsXBzc2O1mlPEz88PRkZGGDp0KNOmqM2DBw/g5OSEDx8+YNq0aQgLC6NsXlbfwsl1yZo1a9C9e3esW7eO9YWcdcmzZ88QHh6O4OBg2vpQLORsZmaGjRs3UnaPcg6vFEB1OHlubq4s0lKq5rZu3ap3D0ZpOLk+LaJOS0uDr68vgoKC0LZtWyxdurRINacMVYY0mQonZztfv37F6tWrcfr0aVhYWGD79u1lWs3Jk5GRgaVLl8LLy4sWxx8dHQ0+n487d+5g1KhRMjVHNZzD03Ok4eQ2NjZat/XmzRsIBAI8ePAAY8aM0Ts1J09OTg4WLVoEgUBQbDg5W1BUc/Jzc+qgykuJPoaT04VEIpHNzaWkpODjx494+fIlqlWrxrRprGLZsmWwsbFB/fr1KWtTJBLh2LFj8PDwkKm5TZs20fpizTk8PYaKcPLSouYUsbGxwfz589G0aVOmTSkSqZoLDAxEu3btsGzZMrRp04bWPvU1nJxqpMniz549iz///BNbtmzBwoUL4ePjwzk7BTw9PVG/fn3KikZHRUVBIBDI1Jyzs7POElJwDk9PIYRg3rx5GoeTv3nzBnw+Hw8ePMDYsWNlEVClAWkme8VwcrZw//59ODk54ePHj5g+fTqlc3PFwWQ4ORsorvTX+vXrMWXKFNpfOPSN169fw8fHR+vlPFI15+7uLiv9RbeaUwbn8PSUPXv2oF+/fiqFk0vndeTVXN26dWFubo5t27bpvZqT5/379zh8+DCCg4MZT70kT1paGnx8fBAUFIT27dtj+fLltDxci7qWTIST65LirrWimlNMFn/hwgXExsZi/fr1OrCUOui+v7Ozs7Fw4UK4uLhonBqNjkLOXGqxMsadO3dw9+5deHt7q7T/mzdvIBQK8eTJk1Kn5uSRhpMfOXJEq0r3VCJVc3FxcZRHWqqDs7Mz2rRpo5NwcjYgVXPOzs4QiUSYM2eO0kLOX79+xebNm/UqsElXrFixAsuWLVM7cIeJQs6qwjk8PSM5ORk2NjYICgoq9gbKzc1FaGgovLy8ULt2bZiammLHjh2suOnoYu3atZg7dy5atGjBWMJsQHdqTlWePXuGY8eO0RpOzhYU1ZyDg0OR2WekWWb27t3LVYdQIDAwEJUrV8aIESNUPoYtpb+Kg3N4egQhBAsWLMDWrVuLjJ6Uzs09fPhQpuakP+bS7OxOnz6NlJQUTJ48GQAz5yqv5nQ5NyePRCIp8Lc0nNzb27vUzttJ1ZyLiwvEYnGBubnicHBwwPDhw9GhQwcdWUotdN3jUseliuplovSXNm1zDk+POHLkCLp3746ePXsW+Fyq5jw9PfHjjz/CwsKiwNxcXl4eE+bqjLi4OOzcuZOR6hCKas7Kygo///yzzu2QovgwWLZsGVavXo169eoxZBF9fP36FS4uLjh37pwsC4qqUbnXr1/H8+fP4e7uTrOV+kVubi7mz58PR0fHYotGM1n6Sxs4h6cnPHr0CBcvXoS/v7/ss8jISPD5fDx69Ajjxo2Dh4dHqZybKw6xWAwLCwscPHiwxHpvVMIGNVcSnp6eaNCgAQYMGMC0KZQhkUhw4cIFODs7QywWY86cOVixYoVagQwJCQlYu3YtQkNDS/WohybY2Nhg3rx5MDY2LrSN7aW/VIFzeHqAfDi5SCRCSEgIvLy8ZGpu+/btenXTUcnGjRsxefJkncyRpaWlwdvbG8HBwejQoQPjak4Z0gd/ZGQkfH19ZUs09J0vX77A1dUV586dw19//VUo0lLVUQzpcp6dO3eW+iLQ6nLs2DHk5eVh3LhxBT7Xt2TxxcEjbIrdppnU1FQYGRkhJSVFb252QgjmzJmDoUOH4uHDhzI1N336dJXVnPRhQEfVZSa5cOECPD094ezsXGgbled87949ODk54dOnT5g+fTrGjRvHOjUH5M/X/fTTTyCEoFu3bvDw8FC7XBCbUKbmBg8erHRuTtXrvXfvXhgaGmLx4sW02KxLqLzHY2NjYWpqimPHjqFixYpKS3/16tWLFS/WiYmJqF27tkbP8dL1BCxl5OTkYOnSpbhz5w4qVKgAc3PzMq3m5Pn69Ss2bdpEWzh5amoqfHx8ZGrun3/+YZ2aK4rs7GwsWrRIb52dvJrr168fdu7cSUmli7t37+LWrVtcdQgFpEWjDx8+jA8fPsgSUui7mlMGp/BYiHRu7tq1a0hPT8fly5e1mhAubQpPIpFg/Pjx2LBhAzp27Kh0H03OmRAim5uTqrnx48ezZk1fSWRkZKBu3boQi8VITEzUq1B7iUSC//3vf3B2doZEIsHcuXMxaNAglRMVl3S9U1JSMG7cOAQFBelFcIUqUPW7tra2RnZ2NqKiomTpBX/99VfWvlhzCq8UkJOTI1s3V69ePcycORP3799HSEgIo5kJ2Ig0nLwoZweod86pqanw9vZGSEgIOnbsqFdqTp6oqCiIRCK9cnRfvnyBi4sLzp8/j379+mHXrl0aqbnirrd0Oc+WLVtKjbMDtP9dv3nzBra2trh+/TpsbGywfv16vVBzXKYVPeb169fg8/l48uQJxo0bB09PT9SoUQPm5ualNpxcG65fv45nz57Bw8NDq3YIIbK5uc+fP+Pvv/9GeHi43qg5RXJzc7Fs2TJUrlyZtW/mUpSpuX///Ze2enOOjo7o3LkzevXqRUv7+oR8esEqVarg3bt3ePXqlV69JGkD5/AYICcnByEhIfD29kb9+vVhbm4OBwcH2YOqNIaTUwEV4eSKau7ff/9F69atKbZU99jY2MDU1BT3799n2pQi+fz5M1xdXbVWc+rw+PFjnD17FoGBgbT2w3YUS385Oztj7ty5cHNzKzPODuAcnk4pSs0p7kN1ODnb3/hVQRpOvmPHDpXG7eXPWarm+Hw+Pn/+jOnTp+u1mlNEGk4+evRozJ8/n2lzCqArNafsHk9PT4eVlRV8fX1LZZaZkn7XiqW/LCwsZKW/Nm7ciPHjx6Nt27Y6spY6uEwrLEaq5ry8vNCgQQNYWFgUUHPySLOTu7q6lpoAE6rYt28ffv/9d3Tr1k3lY1JTU+Hv7y9TcytWrCgVak6emJgY7N+/H8ePH2dVRp3Pnz/L5ub69++P3bt3o0GDBjrrnxCCxYsXY926dahbt67O+mUDytILyi9hunz5Mt69e4c1a9YwaCUzcE9Vmnj9+jWcnJzw9OlTjB8/Hl5eXiUqkxUrVmD58uV6G05OF3fv3sWNGzfg5+dX4r5SNXf06FF8/foVM2bMKFVqTh6RSARLS0tZdQimHZ5EIsH58+dl6yLnzp2LVatWMaKu3Nzc0Lx5c/z5558675sJ5JPFF1f669u3b9iwYYNWRaP1Gc7hUUhOTg6Cg4Ph7e0tU3OqVigIDAxElSpVMHz4cB1Yqj+kpKRg5cqVJVaHSE1NhZeXF0JCQtC5c2f8888/aN26dalWynZ2dpg9ezZatmwp+4yJiFypmvvf//6H/v37Y8+ePTpVc4pEREQgODgYISEhjNmgK968eQMXF5ci1Zw80uoQu3fvLrNV3Uvv00CHvHr1Cnw+Xy01J8+7d+8gFAq5mlwKEEIwf/58bNmyBbVq1VK6/e7du+Dz+fjy5Qv+/vtvWaYIptUO3Zw5cwYJCQmYOnVqgc919dbOJjUnT2ZmJpYsWQIPDw/aoj6ZRj5ZfJ06dWBpaalSIeddu3Zh8ODB6NSpk44sZR+cw9MQZWpu586darcjn528fPnyNFiqv0jDyXv37l3g85SUFFmkZefOnUtNpKWqfPr0CQ4ODoxUh2CbmlPEysoKq1atYpVNVCGdm3v06BHGjh0LFxcXGBkZqTSKcfPmTTx69Aienp46sJS9cA5PTRTVnLe3N6pXr65xe8VlJy/LKIaTF6fmyhLS6hAHDhxAlSpVCm2nY0hTUc2ZmJiwQs0p4uvri9q1a2PQoEFMm0IZxZX+UnUUIzExEatXr+aqQ4BzeCohr+YaNmyosZpTpKjs5GUd+XByaYUCqZpbuXIlWrVqxbSJjLF582ZMmDChyHByKh9onz9/hrOzMy5cuIABAwawTs3JExkZCS8vL0ZULx1QVfpLupzHwcGhzJUOUwbn8Irh5cuX4PP5eP78OSVqTp7Y2FgcOHBAJz9QfUotJg0nnzhxImxsbGSRluqqOX06Z1W5dOkSoqKisHbt2iL30dbhSSQSnDt3Di4uLuDxeJg7dy6sra1Zp+bkyc7OxuLFi+Hk5KTXQUqK6QVLShavyj1+4MAB9OnTBz169KDaXMbgUotRSHZ2NoKDg+Hj4yNTc+qs/VIF+ezkZW1IrjhSUlKwaNEi3Lx5Ez/++CNWrVpVptWcPNJw8vDwcFqGpT59+gQXFxeZmtu7dy/q169PeT90sHLlSixcuBCNGzdm2hSNoKuQ871793D16tUCRaPLOpzD+468mpswYQKlak4ROzs7zJo1q0A4eVmFEII7d+6Az+fj3bt3SE1NxZMnT5TOT5VVJBIJLCwssGfPHkrDyfVRzSkSHByM8uXLY+TIkUybohbqqjl1kS7nCQwMLPPzdvKUaYcnVXPe3t5o1KgRzM3NKVdzipw9e1ZpODmdsPGGT0lJgZeXF0JDQ9GlSxcsWbIEVlZWOHbsGCXOjo3nrCk7d+7EkCFDVAonV2W4R5/VnDxRUVFwcnKiTfXSgaKaU5ZeUFWKG+pcuHAhNm7cqHQ5j77DpRZTk9evX8Pb2xsRERGYMGECfHx8aFNz8kjDycvqejupmnNyckJ8fDxmzJiB48ePo0KFCpg3b16pDSfXhhs3buDx48dah5NL1ZyzszMMDAxgYmKid2pOHulyniNHjqBChQqsXncpr+akyeLpLOTM5/PRvn17/Pbbb7S0r8+USYd3+PBhLFq0CF27dtVZn2KxGJaWlti/f3+ZG65LSUmBp6cnQkND0bVrV9jY2BQYzvXx8Sl14eRUkJiYCFtbW7XCyRUVXlxcHFxcXHDx4kUMHDgQ+/bt00s1p4itrS3Mzc3RrFkzpk0pElWSxVPNkydPcPLkSQQHB9Paj75SJh3e3r17dV7xfMuWLXqbnVwTCCG4ffs2+Hy+TM2dOHECFSpUKLBfZGQkPDw8yqzqLQpNw8l5PB4IITh37hx8fHxkas7GxkZv1ZwiJ06cQHZ2NiZMmMC0KYUoqfQXnaSnp2PZsmWltjoEFZRJh6drylJ28uTkZHh5eSEsLEypmpMnJycHCxcuhFAo1OtwcjrQJJz806dPyM7ORl5eHp48eVJq1Jw8Hz58wN69e1m33o4JNafIkiVLsHbtWvz444867Vef4J4yNFMWspMrU3PSubniWLlyJRYvXqy34eR0oU44uVgslkVaSiQSGBoaokKFCvjnn39KXWFP6XKeQ4cOoVKlSkybU6j0ly7VnCJubm5o0qQJ+vXrp/O+9QnO4dFIac9OrqjmVq9ejRYtWqh0bHBwMMqVK4dRo0bRbKV+oWo4ufzc3KBBg7B//35Uq1atVJeWsre3x99//8143lRNSn/RycuXLxEYGEhp0Wg2Ii39tX//fo3b4BwejZTG7OSEENy6dQt8Ph+JiYkqqzl5oqKi4OjoyLphKaYpKZxcLBbj7NmzcHFxQbly5QrNzWVkZOjaZJ1x/vx5fPnyBRs3bmSkf21Kf9FJVlYWFi1aBHd391JbHUK+9FenTp2wePFijaOWOYdHE2zKTk5Fmq3k5GR4enoiLCwM3bt3h62trcpqTh5pOPnRo0fVcpLqoo+pxYoKJ4+Li4OzszMuXbqEQYMG4cCBA6hXr57SNph+ANPB58+fsW3btmIDm+i63mxTc/IQQrBixQr8+++/aNiwIdPmUEpxyeITEhI0bpdzeDSQlJQEW1tbhISE6PUDSJmaUxZpqQ62trYwMzNjdTg5EyiGkytTc6tXry5z0XfS5Tz79u3T2XIeqkp/0Y2/vz+MjIwwZMgQpk2hDPnSX506daK89Bfn8ChGGk6+fft21mQnV9fpUqXmFDlx4gSysrIwceJErdsqCX160ZAPJ5dWKFBFzSlDH5VtcWzbtg1jxoxBu3btit2PiustLf0Vn3ALCxdXg19QNVQoVxsGPBV+xzmRQIIzkBsNVDAGapsAFenLA/v27Vt4enqWivV26pb+4jKtsIiDBw+id+/eepedXFHNzZw5U2s1Jw9bw8nZwOLFizF48GAsWrQI5cqVg6mpaZlUc4pcvXoVr1+/xurVq2nrQ7H010rr+mjU9CYAHgACMXgQEweUgxCGvDnKG0lwAWLNZMcAPOCrA9BYCNQu4hgtbZZOC+hz0WgmCjlzDo9C7t+/j6tXr8LPz49pU1QmOTlZtvC7e/fuWLNmDZo3b05pH2wLJ2cLcXFxWLx4MR48eIA2bdqoreaUUVoUXnx8PNavX09b0dJXr17ByckJz549k5X+qlrtM0SkDQBJof3ziCkM0Bc8nsKa0pzI786u8DGINQWq9QUqfj8mJRJ45QykRwPVjIGfTQAj9VXgqlWrsGjRIjRp0kTtY5lGPln8169fdV7ImXN4FJGamop///1XL7KTE0Jw8+ZN8Pl8JCcnUzI3Vxz29vaYPn064+HkbEAsFuPMmTNwdXVFZmYm4uPj8fr1a8re1Nl+76mCRCLBvHnzsGvXLkpz3JZU+itPsgX5Kk0ZPIiJEOV4Wwt+nOBc7DFIEAINtwKvXICrCirwiQPwhxBoPUflc5C+AIwePZrV+UMVkU8W37lzZ8ZKf3EOjwL0JTt5UlISPD09ER4ejh49emDt2rWUqzlFzp8/j8+fPzMWTs4WPn78CGdnZ1y+fBmDBw/Gjh07YGpqKitvw/Efe/bsQf/+/dG5c2e1j81GJOLhjFxEowKMUQcmiH4pBp/Px7Nnz4ot/UUQjXxnpAzyfbsCucUfg9zofGV31QwgSlTgFVOgXl/AqORSYe/fv8eRI0f0ZlpAUc1pUsiZavTK4V25cgU7duzA/fv38enTJ4SEhGDs2LFMmwWBQIB27dqxMjs5IQQ3btyAUChESkoKZs6ciZMnT+rkIfv582ds3bq1zObJlFdz5cuXh4mJCWxtbWFgYID58+djxYoVlIeT6/uQ5u3bt3H//n14eXmpfWwCzxWxsATAAwgBIUActuHKrT8xffquEkt/8WCM4tRa/nYFKhR/DCoY5w9jFrfPKyHQc2sR2/MRiUSYN28eDh8+TOtyHipQLP3FpkLOeuXwMjIy0KlTJ8ydO5c1iWOfPn2KkydPIigoiGlTCiCv5rp16wZbW1udDinKV4cobSmuSkJRzR08eLBAfkM/Pz8YGRlh6NChlPetz0OaSUlJsLGxQXBwsNrnkYNIxBpYQjaXxgN4PIBHgL/mXEU7lBxpacAzgZg4FLGVwJBnWvjj2ib5ASpFHIPapsDLtShWBaZHl2jb2rVrMXfuXEqipelAXs19+/ZN53NzqqJXDm/YsGEYNmwY02bIyMjIwLJly2RZ6ZlGqub4fH4BNcfEQ3Dbtm0YPXp0ieHkpQWxWIzTp0/D1dUVFSpUgKmpqUzNyfP27Vu4urqWWdVbFIQQzJ8/H9u2bUPNmjXVOjY7OxtX36zED78QFEo2wsv/n3gI0QjFqygDXiuUgxB5xBQF5tpAUI4nLBywAuQvPWgszA9QUTgGjYX5ASvVjFGswqtmXKxdp0+fRmpqKiZPnlzsfkzAZjWnDL1yeOqSk5ODnJwc2d+pqakA8ocHRCJRiY5AfnhI2b6LFi2CjY0NfvjhB4hEoiL3U6dNZfuWtF9iYiK8vLxw4sQJ9OjRA7a2tgUWdkttU6d/TeyU7nvt2jW8ePECK1euLDSxruo5adM/UPCcqWpTGVI1d+3aNQwePBj79u2TqTmJRAKJ5L95m+zsbMybNw9Hjx4Fj8crNuhAk+uUl5cnW/spFouL/O5LalN+X7qvk5RDhw6hW7du6Nq1a4FrV1ybL1++hEAgwIsXL7D8QAIMDaQOp1DHyCZREIlV+Y3OAI/8CsJzAfAePJ4xeGQuCFoiD4WvFyEEqPE30PJXGCa7AqL3QPmmkPwwN9/Z5eUBLWbB8Em+CpTvmQAAkYA8fALErIKkzxzgx1YFvqdPnz5h586dCAkJKXQ9pd8TIURn10m6/c6dOxAIBIiPj8f06dMRGhoqG2pVdl9Tee8p+22rSql2eFu3boW9vT0tbXt4eKBx48b466+/GJk3kao5Z2dnJCcn4++//0Z4eDjj4/vx8fGwt7fXaFhKX5DOzbm7u6N8+fKYO3cuVq9eXWIuw9WrV2P+/Pl6GU5OJw8ePMCVK1fg6+tb4r7SSEs/Pz/89NNPMDU1RdeuXfERqxGPR0UcxUMFNFXZHh5agkc2f///Kt7DFVtCUn+z8m1GrSDu4wTDGxYgUvVHkB/EEg3w4k8DvDMwPLsTkplOIL1mAci/z+bPn4+9e/eicuXKKttPF8nJyfD29kZ4eDi6dOmClStXykp/6ctvvVQ7PBsbG1hZWcn+Tk1NRePGjVG+fHmtgjZevnyJoKAghIWF6Txha1JSEjw8PHDs2DH07NkT69evLzFNl9Qh011zTiKRYOHChdi9ezd++OEHWvsqCTrO+cOHD3B2dsaVK1cwZMgQHD58WOXaY6GhoTA0NMT48eMps0eRcuXKyUYxDA0N9aLGYGpqKqytrREQEFDsb/LFixfg8/mIiIjAhAkT4OvrWyDSso5oLuKxW/nBPIIfeeYob8BgNGxbU+CnP/MDVOKfAvdOAF8B5BDIHCAAQw8LGP78J/BjS2zevBlTp05F+/btlTYpvcfpDEBTVvrr5MmTjL5YR0VFaXws+38RWlCxYkXKJ02ZyE6uODc3a9YstSItdfX2JQ0n79Kli076Kw6qzlnZ3NyaNWvUmrPVZTi5PkVpEkKwYuMsLHBriAe1F6E6jNEGJqiJ/Dmg7OxsBAUFwcfHB40aNYKFhQW6du2qtK1KvNZoLHFCrKEFFOfSjCFEJZQc9k87Ri3zozGDbYCPpwGJuPA+PB5wTYgLNQchNjYW69evL7I5On/X6hRy1iVZWVlYtWqVxseXaodHB1ZWVrSEkysjKSkJ7u7uOHbsGH799VfY2dmxNuny7du3cffuXfj4+DBtCiV8+PABQqEQV65cwdChQ3H48GHUrVtX7XZ0HU6uTw6Pf8UEnbeHI97AAPHfHdQjOKB13EYc3xlfQM2pUk+yNpkNI/yJeAjl1uGZssPZyRMfDRR1nQhB9seX2Hzojs4DmzQt5KxLVqxYgQULFuDKlSsaHa9XDi89PR1v3ryR/R0VFYVHjx6hVq1aOpkXoTOcXAohBNevX4dAIEBqaipmzpyJU6dOsXpxclJSEqytrfW+OoRYLMapU6fg6uqKSpUqwdTUFOvWrdPqnHQdTq4v3//d1yeQ97sreAb5GSulEAK8rL8GE01D0KddEUOUxVAJLUuMxmScOsb5Sk5ZfA2PhxO3nmPv3iCdLeeRTxbfrVs3tQo565KAgABUrVoVgwYN0rgNvXJ49+7dK1DCXjo/N3v2bLi6utLaN93h5ImJifDw8MDx48dZr+bk0SacnC1I1dzVq1cxdOhQHDlyRCM1pwibw8mZJCMjA573FuKXVoYFnB3wfe0czwAG7W4BGMOMgXTzmwlwWvnaPSKRIK/XbHTo0IFWE+STxSckJFCeLJ5q3r17B6FQiGPHjiEtLU3jdvTK4TEVESnNTs7n8ylVWsrUnK6yoFDF4cOH0aNHD/z6669Mm6IWdKg5eeLi4rBr1y5GhqXYzqJFi9BuWRWIJWIYKJ0GJ0hTlsartFCvFTBbCLiZfld6BODxQAiBIPdXmC+irzoEXaW/6ERaNNrR0VHrZ6NeOTymWLVqFRYuXIimTVUPbS4ORTW3fv16GBsbU9K2Lnn48CEuXLiAgIAApk1RmdjYWDg7O1Ou5uQRi8WwsLDAgQMHdB5OzuYhzRcvXmD5okWIjI5Gr6U/gxi8LqTw8uGhurI0XqWF95HA/VeA0TCgfAJQtzayfmwJc7dbOBx4mvJrSEchZ11ibW2NefPmUfKM5BxeCYSGhgIAxozRbniFEIJr165BIBAgLS1N7UhLtpGWloZ//vkH/v7+rMgyUxx5eXk4deoU3NzcUKlSJZiZmVGq5hTZuHEjpkyZgjZt2tDSvj6RlZWFoKCg/GUEaWnIeP0ar2JjkV4uCr4o6vsh+AVK0niVBkJdgA1mhZSdc92usNrmiBo1alDWlT6qOUXCw8ORl5eHcePGUdIe5/CK4f379zh8+LBW4eSJiYlwd3fH8ePH0bt3b9jb2+ulmpNHWh3C3t4ederUYdqcIomNjYWbmxuuXbuGYcOG0aLmFLlw4UKJ4eRlgYiICPD5fLx8+RITx42DS/PmmHbgAHyFQpQrVw410Qp/QYhLKJyS6y8IYcS2yEoqeB+Z7+wkhasmzP96HwZ1tHd2dBdy1iUxMTE4cOAAjh8/TlmbnMMrAmk4+ZEjR9Rey6dMzTEZaUn1vI6zszN+/vln/P7775S2SwVSNefi4oLKlSvD3NwcdnZ2Ohnq+/r1KzZv3sxonkwmhzSlas7HxwdNmzaFubk5utSpA0ybhoXXr8OqWjX8NGOGbP82mIMG6IsXECIN0agOY/wCU42cnT7MXSLMOV/ZKcADAAMDIFQILFE9wlT+nHVRyFmXiEQiWFpaKn3+anOtOYdXBJqEk5dGNafIs2fPEB4ejuDgYKZNKUBsbCyEQqFMzR06dAh16tTR2UuGRCKBpaUl9u7dWyqrQ3xBJK7CGfGIRh0Y43eYoN73BeIRERFwcnLCq1evMHHiRPj5+eWvmztxAhg4EAGJiagKYPjMmYCC0jBCS/Ri+zICqoiLLnL9HY+Q/O1qIFVzLi4uOinkrEvs7Owwe/Zsyhe7cw5PCadPn0ZKSopK4eSKam727Nk4ffq0XqR1UpeMjAwsXboU3t7eOk+ppgypmnN1dUWVKlVgamoqU3PaJJjVBAcHBwwfPpz2cHImuAoXuMIMPPBAQMADD6eIA36+YYrLWz6iadOmsLCw+K9gq0gErFgB7NqFdwCEAI4BwMyZjJ0DK2horFThAcj/vKGxSs1IS39J183popCzLjlz5gwSEhIwdepUytsufU9lLYmLi8POnTtLnLdLSEiAu7s7Tpw4gd69e2PDhg2URXFSDVXDXMuWLcPq1atRr149StrTlNjYWAgEAly/fh3Dhg2Do6NjoblEXQ7tXb9+Hc+fP4e7u7vO+iwKiZL5IW34gki4wgwEEtk66e/ZH/GytwAH/R+iWdVO/x3w/j0wZQpw+zZyAcwH4AigfIsWQK9elNomD5ujU2WMMQFci6idRwgwtuhAHUIIbt68CT6fj6SkJMycORPHjh1D+fLlS9XL9adPn+Dg4FDs81eba116vikKkIaTHzx4UGk4OSEEV69ehUAgQEZGBmbNmlVq1Zwinp6eaNCgAQYMGMBI/3l5eTh58iTc3NxQtWpVmJqaYv369Yw/6BISErB27VqEhoYybgtA/YP/KpzBIzwQhWZ5PMCAZ4D7VX3RDN8dXlgYMGcOkJwMALAGMA/IX2AwY0bR6qas0LQVYCcEWW8KCSEwMODlXy9CADsh0KTw8J18IecePXoUUHPFlZfSR+SX81SpUoWWPkr/k1oNNm7ciMmTJxcKJ5dXc3369MHGjRtZq+bo4PXr1/D19ZUt0dAlMTExEAqFuH79OoYPH65UzTEFIQTz5s3Dzp07KQ0nZwvPnz/H2exgiDuLwVMygk1AEI9oIDcXWLkS2LdPti0cQB4AWTC5XLBKWSZ9wETM3+MIx6E9USX5a/4w5ljTAs6uqELO+rqESVU2b96MCRMmoG3btrT1wTm871y4cAExMTGycPKyrObkyc7OxsKFC+Hq6qqzc2ermlNk3759+OOPP4rM4M8E2kYrZmVlISAgAH5+fjA2Nkandb/hoeFbSJQsEOeBhzowBqKigPr1genTgXPnEPPtGw4AkAWT9+oFsCDTPtMQQrB48WKYb9iOKn/8UWi7YukvfUkvSAWXLl1CVFQU1q5dS2s/ZevpXQRfv37Fpk2bEB4eXubVnCIrVqzA8uXL8dNPP9HeF5vVnCJ3797FrVu3WFcdQtOXgufPn8PJyQmvX7/GpEmT4O/vj6pVq+ILIvEAbkqPISD4HabAzy0Ba2vg7VuIjh2DJYAjAGTB5GU9WOU7rq6uaNGiBf6Qc3ZSNScQCJCcnFxm1Jw83759w4YNGxAeHk77S22Zd3gSiQQWFhaYMWMG5s+fj8zMzFIdaakOgYGBqFKlCoYPH05bH4pqzszMjJVqTp6UlBSsWrUKQUFBrLazJKRqztfXF82aNYOFhQU6depUYJ96aIW5EMIFpgWiNAkI5kKIetI1czk5wJQpsEtLw2wALdu3B549A8qVA8pq8uxzF4B124C4L8j8oTreVQLWX78MoLCaW7duXZlRc/JIn7979uxRqQSUtpTpJ3p8fDxmz56Nd+/e4f3799i8ebNOygzpA9Ls5HQtoo6JiYFAIMCNGzcwYsQIODk5oXbt2rT0RSWEECxYsABbtmxhvKq7MlQZ0nz27BmcnJwQGRmJyZMny8quFEVfzEEr9MVVCOXW4Zn+5+wAwNoaZ+7fRwKAqa1bA9evA3/+CTRpArBUpdOKySLAJRBAfkRr5Zgv2ADgy9hpsKlTFcnJyXqfXpAKdu7ciSFDhhR60aKLMunwrl27Bh8fH8TGxgIAnjx5UqpvOnXndajMTi5PXl4eTpw4AXd3d5mas7e3p0Ul0ZV5w9HREZ07d0YvGkPstaGovKZZWVnw9/eHn59fkWquOOqhJSYWtUA8PByf9u6FA4BjFSoAfn5AjRqAvX1+QIsOYFWmlXMXvju7/PtaencTENQ7fgVbPPagwYxpWnfDqnPWgBs3buDx48fw9PRU6zgu04qaXLlyRTY3FRoaWqqdnSbY2NhQlp0cyM9JKhQK9U7NKfL48WOcPXsWgYGBTJuiMlI19+bNG0yaNKlENac2MTEQz54NCwAHAFTZuxeQLkAfNSp/EXoZQSIhSMgUoar1ZlTGf45OCu97rtAGh1wAChyePpOYmAhbW1udL+cpkw7PxsYGZmZmpTacXBuOHTtGSXZyqZpzc3NDtWrVaFVzuiA9PR1WVlbw9fVlbXWIGN4b1FiXBcPGEix4PRFxhzLxc6UOMDc3p2fISCQCpk3D5uRkTADQduJEYN68/7bzeIVSiekradl5uB6Vii9pufiSlouv6aLv/1+EL+n5n31LF0GSlYro569R7MRI3Bddmc1KpMt5HBwcYGRkpNO+y6TDO3LkCOvCyelEVScTExOD/fv3a5Wd/P379xAIBLh58yZGjBgBPp/PiJqj0rFKw8nXrVtHe7UFTQmBC9ZVNkO1xRKABzzgnQWPDyzkzUUn0DQ/sm4dLt24gSgAa42NAT6fscXldL9IVa1giAuRSdhx8UPhjYQAcU+BZyeA3Ex8rFwdTXISi26sITWZivT15fHAgQPo06cPevToodHxXKYVNbl7965eDUvpguKyk5dEXl4ejh8/Dnd3d1SvXh1mZmbYsGGD3v4gFXFzc0Pz5s3x559/Mm1KITIzM+F0+gAEY60BA4D3/RctTQW2Dqboir5oQnW5nTNn8G3bNmwAEF6uHHj+/kDNmtT2wSIMDHhwGN0CdaqWx6rjUfkfZqcCL84CUTeB+r8Aveagcp2fkNX0K7BooSyi9T++zz1toq+iOdu5d+8erl69Cn9/f0b6L5MOb/fu3aXmYUwVmmQnl1dzI0eOZEzN0UlERASCg4MREhLCtCkFePr0KZycnPD27VvU38aDIc8Q4iIWhwdBiOVUViSIi4NkxgxYANgDoJqDA6Dh27q+8OJLBvg3P8H1zmfg4xOZmsMvg4Ex2wHDcmj6Q0WEmLRD1J1zuNO+CX59FgOZk5NiOgkY8BcTp8A4KSkpWLlyJQIDAzV6/orFYpw6dQp8Pl9jG8qkw2NjODmTqJOdXCQSySItS6OakyczMxNLliyBh4cHK6pDZGZmwt/fH/7+/mjRogXMzc3RsWNH/ItpIIoP1u8QEMQhmjojxGLg77+xMz4eQwB0GjkSWLaMuvZZRLZIgqAn3+B44xOuRsQCEWfy1VyDdkCvOYBRA9m+A1vXhM/Mtkj79gFOTk4Iv38NuHoDWLMlf86uYb18ZVdGnZ20aPTGjRtRq1YttY5VLP21c+dOjZdLlUmHx/EfqmQnB4Do6GgIhUKZmhMIBGrfuPqGlZUVVq1ahQYNGpS8M43Iq7nJkyfLEgJIaQhjhaGz/+CBh4b56ZupYdMm3Lh0CY8BeP70E+DqWuqSQr/4kgGnG5/gdvczkt48LKDmKk7aiYld6sPr/lfZ/iv7N8bm4c0gEYswY/58HDlyJL8m3YC/yqyDU4TP56N9+/b47bffVNpfWvrLzc0NlStXLlD6KzGxmPnREuAcXhmmpOzkimrO3Ny81Ko5RXx8fFC7dm0MGjSIkf6las7Pzw8tW7aEhYVFkbX2xsMELnDIHz1TuDQEBBNQdNkZtbh4EYnr18MWQKiBAXi+vkApGcLOFkkQ+PgbnG4qV3NtW7eAZZ8GmNGtHvIkBF73v6JKBQO4TP0Zk7v8CAD419oW5ubmZTJjSnE8efIEp06dQlBQUIn7Kqq5o0ePUppekHN4ZZiispNHR0dDIBDg9u3bZUbNyRMZGQkPDw/asswUx9OnT+Ho6Ih3795hypQpCAoKKrFUSlO0wgYIsQ6mEOfl18MrZ2gIwiPYACE1AStfv4JMn455ABwAGG3aBPTtq327DBPx+fvc3N3PSJZXc22HoOLknZjSpQEsejdAn2Y1ZC96zz9loEWdSgiZ2w4dGuanwzpx4gSys7MxYcIEJk+HdaSnp2P58uXw8fEpcjmPopozMzOTqTmq4RF9X66vBqmpqTAyMkJKSkqZWn8nrZslnxv00qVLcHNzg7Ozs6xCuDTS0sjICGZmZvjtt9/0Vs0pO2dVyMnJwahRoyAUCtG4cWM6TCtEZmYm/Pz84O/vj1atWsHc3FyjyukvM59g8NGeKNdEgnmjl2BqhXnUODuJBBg2DPvPnoUEwLLBg4FTpwAWrUdU53pn5YoR9CQejjficC0i9r9IywbtgPYj0LZVc1j2aYCZ3evhhyoKSSkiPyL9yElUiP2GCi3rAyZD8KEywdy5c3Hs2DFUqlSJjtNTiqb3uC4xNTXFzJkz8ddffxXaJlVz0kLOs2bNUknNJSYmonbt2ho9xzmHVwYQfc92Ic0o8+3bN0yZMgXh4eGIj48voOZmzpxZKtSc4jmrytKlSzFw4ECMGjWKDrMK8OTJEzg5OSEqKgqTJ0/GpEmTtCp8mZGRgUaNGgEAPnz4QF1GlW3bcM/GBtsB+NerB96TJ8CPP1LTNkWocr0jPmfA6Wb+3Fxy5APg+QlAlJ0/N9e6D6Z0aQDLPg3Q27iG8hc9l7OA2Z78OUtCAB4PhBDsbQ+MCNiH1q1b03V6StH0HtcVbm5uiI6Ohp2dnewzeTVXpUoVmJqa4o8//lDrxTohIQF16tTR6DnO3lcDDlqQSCQwMzOTOTepmtu4caPeqjmqCAkJQfny5Wl1dhkZGbJIy1atWsHS0lIjNaczrl9Hiq0tVgIIBMDz8WGdsyuOrFwxAh/Hw+mmgppr2B7obYJ2rZvDsndDzOj+Y2E1J0/kx3xnJyH4b6lB/r/LngI8A/oz/esTL1++RGBgoKxotGLpL6rn5lSFc3hliOjoaJiYmCAuLg79+/eHUCgsFWqOCqKjo+Ho6EjbvJ1UzakzN8c4CQkgU6dioUSCjQBq2dkB/foxbZVKFKvmJu/E1K75c3NFqjlFnM98j0YtOCDGA/KHdoWnga0mdJyK3pGVlYVFixbB2dlZll6QLYWcOYdXyhGJRAgNDYWXlxdEIhHKlSuHiIgI1uaDpAp1flQikQjz5cPJKSIjIwN+fn4ICAhA69atMW/ePLRv356y9pVB2QwFIcDcueB/+ID2AH776y+A5mrU2sDj8ZCVK4bvoy/aqzllRH/J/06UQb5v1zFsHZGxsLBAvXr1YGJiQkshZy61GEchoqKiIBAIcOfOHQwfPhzbt2/HvHnzEBoaWuqdnbrY2trCzMyMsnDyx48fy+bmpk6dWkDNReINXOCBaMTAGE0wFzPRiuq0X1Swbx+eHDuGkwCCa9cGvLwAFiy+V8bzTxlwu/MRvg+/Ivb5/fxIy7wc4Jchmqk5ZRjXU6rwAOTLPGNq8mPqK9JCzps3b0ZGRgYOHTqk9tycLuAcXilCJBLh2LFj8PDwQM2aNWFmZoZNmzYhLy8P06dPZyQ7Ods5efIksrKytA4nV1Rz8+fPL6TmXOABCywqUDl8B/aCj0OYgxla9S+FEoV39y7S//0XywD4AjDw9AQaNtS+XQqRzs053ozD9YhYVHx9BnnvbgH1OwB9zND+5+aw6NVAMzWnDJMhgEOA8m2EAKZDte9DD5Ev5Pzrr7+iRo0auHbtGmsDaTiHVwqQV3OjR4+Gs7NzgfRpBw8eRK9evTTOTl5a+fDhA/bu3avVvJ1UzUVHR2PKlCkIDg5G5cqVC+0XiTewwCJIICm0zRwL0Re90RItNLZDitZv1CkpwJQpWJKXh7UAfly1ChjKnof580//zc2lvPlPzRl2GAKj6TsxvEO+muvVVAs1p4xWPwHC5SCmeyAhBAY8g++CjwDC5UBLdr0Q0ImyQs6rV6/G6NGjIRQKWevsAM7h6S1SNefu7o4ffvgB5ubm2LRpU6Ef+b1793D9+nX4+PgwZCk7ycvLg6WlJQ4ePKj22ilFNbdgwQK0a9eu2GNc4FFs+i9nuGML7NWyg3IIAczM4BYVhSYA+vXuDWzcyKxNyFdzAd+zoFyPiPk+N3cLaPifmlvYux4mda6L2tXpWwcXP7IrlvfMhaDPJFSMS8ofxjQdWmacXXGFnJctW4ZFixahSZNiKwEyDufw9IyoqCjw+XzcvXsXo0ePhouLS5HJsKXZyX19fVk3ls409vb2+Pvvv9VaO/X48WM4Ojri/fv3mDp1apFqThnRiCk2wXM0YlS2ozi0GtJ0dMTLwEAEAAirWRPw8QEYfFsvSs2h7VBUmrwTU7v9p+bE4sKVIqhEIpFg3rx5WHNkFypKK7qXAZSpOcVCztKq5aNHj2bQUtXgHJ4eIBKJEB4eDg8PD5ma27x5c7FOTJvs5KWd8+fP48uXL9iognpJT0+Xqbk2bdpg4cKFJao5ZRijSbEKz7j4Gtkqo/GLzePHyFq6FIsAuAMwdHUFmjalxCZ1KKTmIs4A0bcLqDnL3g0wo3s91Kysu8fXnj170L9/f3QuI86uODWnuN/hw4e1KhqtSziHx2LevXsHgUCgkppTRD47uTQFEQfw+fNnbNu2rcR5u0ePHsHJyUmm5kJCQlRWc8qYi5nYgb1KtxEQmGCWxm1rTXo6MHkyrHJzsQJAw6VLgTFjdGpCATUXeQ94fvI/NddzEqZ2awDL3g3xa9PqOh+tuH37Nu7fvw8vLy+d9qtrpGrOzc1NVvpLUc3JI180msrlPHTCOTyWIa/matWqpZKaU+TJkyc4efIkgoODAVC4NkuPUHbOYrEYlpaW2Ldvn9JF31SpOWW0QkvwcQjmWFggSpOAgI9DlASsABooPEKA+fPh9/o1agIY2q0bsH07JbaUhFTNOd74hBsvCqu5Dj/n57T8u1vJao6uezwpKQk2NjYIDg5m3bQAVeesaSHnNWvWwMTEBC1aUHPvqoo25805PJbw7t078Pl83Lt3D2PGjFFLzcmTnp6OZcuWwdfXl1tvp8C2bdswZsyYQk7s0aNHcHR0RExMDCVqrijmYAb6ojec4S5bh2eCWZQ5O41wc8NbT0+4AQirVg3w8wMqVqS1y2ff1Zx7EWpuWreGsOjdgBE1Jw8hBPPnz8e2bdtQs2ZNxuygg7y8PFmyeE0KOZ86dQppaWmYPHkyzZZSC+fwGEQkEiEsLAyenp4yNbdlyxatfuRLlizB2rVr8aNcvkO2vZnqAsVzvnr1Kl6/fo3Vq1cDyH8x8PX1RWBgIH755RcsXry4UJkkOmiJFrRGY6r19hsRgZwFCzAfgABAeaEQoOltPTNXjIBH+XNzBdTcTx2B38zRoXUzldWcMtS6xyMTAOf7QHQyYFwTMOkGtCqsaA4fPoyePXuiZ8+eatujCzT5XUsLOd+6dQsjRozQqPTXx48fsWvXrhKLRtMFl2lFz3j79i0EAoFMzbm6ulLyBunm5oYmTZqgn57kO9QV8fHxWL9+PUJDQ2VzczExMZg2bRptao71ZGYCU6ZgVVYWFgFoYmkJ0PC2XljNnQDycplTcy4PALPQ/Owo0oK5DtcA4VhgTlfZbg8fPsTFixcREFDEYnM9gspCzvLLefTxd8M5PB2Rm5uL8PBwStWcPC9fvkRAQADCwsIoaa+0IK0O8dtvv2HSpEk6VXNMoLLCW7YMoc+egQdgdIcOwJ49lNkgVXOONz/hZkQM8OI0EH3nu5qzkKm5Gd3qwUiHkZaITMh3dhIl35FpKNC3KdCyNtLS0vDPP/8gICBAr0dH6CjkvHHjRkyZMgVt2rShyErdwjk8mpGqufv371Oq5uSRZid3d3eHIUvzHTLBw4cPsXTpUqSkpGDixIlYvXq1Tgt0MoFKD2gfH7zn83EEwLHKlQF/f4CCt/VnnzLgeCMO7nc/I/XN/Xw1JxYBvwxB5V+nYNr3dXM9mzA0N+d8H0WsDMn/XHgfZMsgLFy4EBs2bFApcINtKCvkTFXprwsXLuDDhw+wt2c4QYIWcA6PBqRqzsPDA3Xq1KFczSliZWWFFStWoCHL8h0ygXRuLiAgADVr1kStWrVw/fp1vX5Tp5TISIjMzTEPwGEAFY4eBbR4W8/MFcP/+9ycMjXX8edmsOydPzenUzWnjOhkpbmfAXyveJAMZ2dntGnTBn379tWhYdqjqOaoLv315csXbN68mbbyWbqCc3gU8vbtW/D5fDx48ABjxoyBm5sb7dFdfn5+qFmzJoayKN8hEzx8+BBOTk6IjY3FtGnTIBAIMGvWLISEhJQpZ1fskGZODjBlCtZmZGAugBazZwOzNFv/9zQuXTY3V0DNtR3KDjWnDOOaxSq8b1XzcOzYMdlyHrYjnZvz8vKitZCzRCKBhYUF9u7di6pVq1Latq7hHJ6W5ObmyiItpWpu69atOvmRv337Fm5ubmV23i4tLQ2+vr4ICgpC27ZtsWTJEvzyyy8ghGDq1KnYvHmzxi8ckfgAZ5xEND7DGPVhguFohUbUngANFHvf/fsvTj98iFQAk9u0AQ4eVKvtgmrufX6k5fs7wE+d2KfmlGHSLT9ARQmEAFbPveAY6sz65TxSNXfr1i0MHz6c9kLO27dvx8iRI9GhQwfa+tAVLLwr9YM3b95AIBDoVM3Jk5OTg/nz50MgELA6OzkdPHjwAE5OTvjw4QOmTZuG0NDQAnNzhw8fRvfu3TUOJ3fBKZhhR8FAPvhCiH8xB8MoOQedExKCuAMHsAtAeMWK+evtqlVT6dCCau4e8OwkIPmu5nrlqznL3g3Qg01qThmtaudHY5qG5te2I0QWrenaNxlz1lmhXj121rWTn5uTlv6ys7MDj8dDuXL0PcavXbuGiIgIuLu709aHLuEcnhrIq7m6devqVM0psmrVKpWzk5eGTCtSNRcYGIh27dph6dKl+OWXXwrtJw0n9/b21ui8I/EBZtihtIyPKXagLzqgJYuVntJ7MToa4rlzYQHgAIDK+/cDHTsW245UzTneiMMt6bo5qZrra4FOPzeDZZ+GmN71R1aoOZWv9Zyu+dGYwv/W4YXW+YColGjMHTCAVhs1Qb7016hRowqoOZFIROtvOyEhAevWrZMlh2YLXKYVmpFXc2PHjpVFQDGFPmUn15b79+/DyckJHz9+xLRp0xAWFlZkpCUV4eTOOFl8IB9OYissNGqbEUQiYOpUbExJwRQAbaZMAczNi9z9aVw6HG9+gsfdT/lzcwpqbvr3uTnWq7niaFkb2DoYAPDq1SvwrfaxalqgqELOuvy+CSGwtLTEzp07UaNGDZ31SzecwysCNqk5ed6/f48jR44wluVAF6SlpcHHxwdBQUFo3749li9fXuK6H2l1CGk4uUgk0qjvaHwuPpAPnzVqlzFsbXHh9m3EAljfogXg5JQ/nCdHRo50bk6q5k4D7+8CjTqzUs1RRVZWFhYuXAg3NzdahwVVRVHNKRZy1iV79+7Fn3/+ia5du5a8sx7B/FVmGW/evAGfz8fDhw9ZoebkEYlEmDdvHg4fPqxWdnKmnbSqyKu56dOnF6vmFFEMJ9f0nI1Rv1iFZ4z6GrWrKwoM95w8ia87dmAzgPBy5fLn7eTe1p/I5uY+IU2a01KSB7Qdhsq9puqVmtPEvhUrVsDKygo//fQTDRaphqqFnJVB1zW5c+cObt26BV9fX1ra1xadpxbLyspCYmJioRvl+fPnlGWX1yW5ubkIDQ2Fl5eXTM1t27aNdT/ytWvXYu7cuTrPTk4nmqg5RZ49e0ZZOLkJhsMByn/oBIAphmvdB51IHR7v40dIZs6EJYC9AKru2gV06yZTc44343BbUc39Pg+dWhvDsk9D/N3tR9SoVHrfhwMCAlC1alUMH87M9VSnkLMuSU5OhrW1NYKCglj3/KMEoiYBAQGkUaNGpGPHjqRDhw7k1q1bsm1dunRRtzmdkpKSQgCQlJQUQgghkZGRZOXKlWTw4MHk8OHDJDk5mWELi+bUqVNk/vz5Gh0rEomISCSi2CLtuHfvHrGwsCAjRowgXl5eJCsrS6N20tPTSf/+/cnnz58LfK7NObuQk8SA9COGpP/3f/sRA9KPuJCTGrWnK9LT04mRkRH5wciI5PXpQ7YCxAkgZMwY8vhDKlkQ8JpUX3WZYPwugp8HErT6i2DMNlJlxUVi5vuS3HmfQiQSCdOnoRHqXO+3b9+SIUOGkNzcXJqtKkhubi4JDAwkY8aMIXPmzCHXr1/X6vum+nctkUjItGnTyM2bNylrkw4SEhIKPMfVQW2H16lTJ/L161dCCCF3794lbdu2JV5eXoQQQjp37qy2Aepy6NAhYmxsTCpWrEi6du1Krly5ovKxUofn4uJCRo0aRUxNTcnt27dZ/yP/+PEjGThwIMnMzNToeLY4vNTUVHL06FEyePBgYmVlRV68eKF1m2ZmZuT8+fOFPtf2nCNJLLEmjmQqsSfWxJFEklhtzNQJUoe3xciIXAPIDICk1mtIBm26QGARQtDXkqBxV4LeJgRmAaTzjnvkyLWPJCWL+XujRF6nEWL9nJCp9/L/fZ1WYLOq1zsnJ4cMHjyYREVF0WRoYd6+fUtsbGzIwIEDyf79+0liYiIl7VL9uz58+DBxcHCgrD260KnDa9u2bYG/4+PjyR9//EHs7e1pV3i+vr6kfPnyhM/nk4iICLJ06VJStWpV8v79e5WOlzq8Xbt2sVrNyZOXl0dGjBihlXNg2uHdvXuXmJubk5EjRxJvb2+N1ZwiHh4eZO3atUq3MX3OTJCenk5G1KhB4qpVI/0A8g088sufiwl+HkDQqh/BmO36qeac3xNiEEaIYXjBf13++92rer2XL19OgoOD6bSWEEK9mlMGlff4w4cPybhx44hYLKakPTrRxuHxCFFvUUO/fv2wb98+dJRbx5Obm4vZs2cjICAAeXl5FA64FuTXX39F165dceTIEdlnv/zyC8aOHYutW7eWeHxqaiqMjIwQFxenN6G2mzdvRvPmzTFt2jSN2xCLxQCg08TSaWlp8Pf3R3h4ONq1a4c5c+agdevWlLUfGRkJGxsb+Pr6Ko2wY+KcmSYjKQnpHbtiSVoSmuflIczoJ8S0HQK0G4aOrZrApEddTO5YGzUq6c93wnuTicpdb4KnsCySAIABkPWwN0iLKipd7xMnTuDixYvYuXMnbfZGRUXBzc0N9+/fx/DhwzF16lTa5uaousfT0tIwZcoUuLm5oW7dulSYRitJSUlo3LgxUlJS1H6Oq+zw0tLSUL16dXz48AHlypVD/fqFo9WuX7+O3377TS0DVCU3NxdVqlRBQEAAxo0bJ/t86dKlePToES5fvlzomJycHOTk5Mj+Tk1NRePGjWFkZAQejweSr3Blk7Py/x8oGA0kkUiU7kcIKZCKSP7rVNa2fJvSfYuyIS8vDyKRSFZ3qqj9FNtU3E8aZZqamkrrORFCkJeXh9zcXBBCUL58eVkWGEVbSzr34s5JIpEgKysLlStXhoGBgdJzqlGjBgghSEtLo/06UXFO2t570u/eQCTCTzxDTK/XErvGbgGiboI8Pw1ewlu9OycAWJs1EUtyhqMcCj/U8yDGgYqnsKFygOx6p6amKrVBes/I54Kk6pwIIRCJRMjNzQWPx0OFChVgYGBQ4NrQce/VqFEDPB5Pds6anBMhBFlZWahQoYLsxZHp515J91716tXx8eNHjRyeymFYv//+O06fPo1GjYrOMkGXswPyi3iKxeJCqX/q1auHz5+Vr43aunWr3paykEgkyMnJ0YtkrYQQ5ObmQiQSwcDAABUrVizgiNQcRCiR7Oxs2UOlrCORSJCbm4u8vDzweDwYGhqC/DkLwoQvgLc5IMr6nkJLPyPumkjqgFfkQpH87SUhfahXrlxZ9pCnArFYDJFIBLFYjPLly8tewKR96gPS3ywb1iHqApXPsnv37vj1119x5syZAmHjDx8+hK2tLU6ePEmLgYoohsoqvnHJY2NjAysrK9nfUoX34sULVg9pSiQSTJs2DWvXrkX79u21bk86zEzlTU0IwYMHD+Di4oIvX75g0qRJGDNmDCpWrEhZH8oICQnB/fv3sWnTpmL3o+Oc2YJEIsHly5fh5uYGsViMmTNnonv37pg2bRqePn2KL7f98OrVK714WSqJ8nZvYLA3BhAXdiCGhoYYtWQKPtjbFnu9169fj3bt2mHSpEla2yPNaenn54cffvgBc+bMQc+ePRkJ4df2Hn/x4gXs7Ozg4+OjF0P/6enpCAwMREBAAD5+/KhRGyp/UwKBAPb29ujbty9CQ0Px448/Ys2aNQgKCtJJiqs6derA0NCwkJr7+vVrkQlfK1asqPQBXLVqVVY/DLZu3YoxY8bg119/paQ9adYRKpJMp6amwtvbG8HBwejYsSOsra3x888/a92uKrx79w5eXl4IDw8vdC6R+Apn3EY0EmGMWpgp6oZWqFuqEmt/+fIFLi4uOH/+vGwuvWHDhiCEYMaMGdi4cSPGjx8PgP33uMpYtgD2vFe6iUeACvNaoELVqkXe42fOnEFqairmzJmjlRnSQs737t3DmDFjZGm/mESb33VmZiasra3h6enJ6pd/4L/SXzExMZg2bRo8PT3RuHFjzRorNqRFCVu2bCGVKlUi5cuXJyNHjiT3799XtwmN6dmzZ6G1aL/88guxtrZW6XjFdXhs5OrVq2TGjBmURnTl5uZqteZIIpGQO3fuEDMzMzJy5Eji4+NDsrOzKbNPFYoLJ3cmN4kBWUoMybL//pUsJQLRdZ3aSAdisZicPXuWTJ06lUyePJmcOnWK5OXlFdjnyJEjxMHBgaSnp5OaNWuSmjVrkvT0dIYspgGXkqM0ld3jcXFxpH///iQjI0OjbnNyckhAQAAZPXo0MTExITdv3mRVZKs2v2sLCwty7tw5ii2ijrS0NOLk5EQGDx5Mli1bRp4/fy7bFh8fT/+yhLi4OLJ48WJSuXJl0rVrV1KlShXi6empdofaIF2WIBQKSUREBFm2bBmpWrUqiY6OVul4tju8+Ph40q9fP8rt0zR8OSUlhRw5coQMGjSIrFixgrx69YpSu9TByspKaTj5a/KFGJClBGRJwf8kS4iBZCmJJF8ZsFZ7Pn36RLZu3UoGDBhANm3aRD5+/Kh0P/lw8vT0dFKjRg1So0aN0uXwCCEkUmEdXmTx6/Dy8vLIyJEjCzwoVeXNmzdk1apVZNCgQeTgwYMkKSlJW+tpQdPftZeXF7G1taXBIu25f/8+sbS0JCNGjCCenp5KlzDpZB1epUqVSOfOncnx48cJIYScPn2a1KhRg2zbtk3tTrXh0KFDpGnTpqRChQqka9eu5PLlyyofy2aHJ5FIyIQJE2hRzOr8MNig5hQJDw8nS5YsUbrNmoQTQ7KssMMjS4ihZBmxJuE6tlZzVFFz8qSmppJ+/frJEkFIF54bGRmVPodXAor3uL29PXFxcVH5+JycHOLv789aNacMTRze69evyfDhw1m1RjU1NbWAmouIiCh2f20cnspzeC4uLpg6dars7yFDhuDixYsYOXIk3r9/j8OHD2s2pqomCxYswIIFC3TSly5hOjt5amoqvLy8EBISgk6dOuHff/+ldN2cpsTGxuLAgQNFVoeIRiJIEfUNCAiikUineZTw+fNnuLq6yubmdu/ejQYNGhR7DCEEixcvhp2dnV6sndIlly5dQlRUFNauXVvivkwXctYl2dnZWLBgAVxcXFgRzKVYyFmdZPGaovJZyzs7KV27dsWNGzcYS8BaWmAqOzkhBHfv3gWfz8eXL1/w999/49ixY7RHWqqKSCSChYUFDh8+XKRNxqj1PWy9sNPjgQdj1KLZSs2QSCT43//+B2dnZ0gkEpiYmGDlypUqL7VwdXVFixYt8Oeffxb4nOhJODxdfPv2DRs2bEB4eHiRkZPypb/q1KnDmtJfdLNy5UosW7as2KVldKNqIWe60NrNGxsb4/r161TYUiZhIjt5SkoKvL29WafmFLGzs8Ps2bPRsmXLIvcxwa9wwP8KbyD5Cs8UvWi0UH0+f/4MFxcX/O9//0P//v1VUnOKREREICQkBCEhIYW2lfaHdnFIJBJYWFhgz549qFatWqHtimqOTaW/6CY4OBgVKlTAiBEjGOlfnULOdEKJrmVDWQt9hBCCBQsWYMuWLbR/h4QQ3Llzh7VqTpEzZ84gMTFR6ciCPK3wI4SYBlP4gAceCIjsXyfJZLQ0ZH64TyKR4Pz583B2dgYAzJ07F6tWrdJo4XxmZiYWL14MT09PvVg7pUt2796NIUOGoFOnTrLP2FrIWZdERUXByckJ4eHhOu1XvvRXu3btNCr9RTXMD+SWYY4ePYouXbqgVy/6VEhKSgo8PDwQFhaGLl26sFbNyfPp0yfs2LFD5aruc/Ar+qI5hLglW4c3W9wDLVFyFg46UVRze/bsUVvNKbJ8+XJYW1sX2U5ZHdK8ceMGHj9+DG9vbwDsLuSsS3JzczF//nwcOXJEraLR2qBNIWe64RweQzx69Ajnzp1DYGAg5W3Lq7mvX79iypQpCAkJUTrMwzbEYjEsLCxw4MABWQ5RVWiJutiKUbK/RURUZDALnVCp5hTx9vZGnTp1MGjQoCL3YUW6tcg8wDkLiBYDxoaASWWgFX2PmsTERKxbtw7e3t4ICAhgfSFnqlDl5Wb16tUwNzdHs2bNaLWFikLOqqLNSx3n8BggLS0NVlZW8PPzo/QBlZKSAi8vL4SGhqJz585YtWoVWrVqJcvIoA9s3rwZEydO1OlENhXQoebkiYyMhKenp86HpdTGJRMwS4UsjogHwCEDENYA5lShvDvyPctMo0aNMHv2bIwbN67MqjlFjh8/jpycHEyYMIG2Ptis5pTBOTwdQ3U4uaKaY/vcXHFcunQJ0dHRWLduHdOmqISimjMxMaFMzckjDSd3dnZmRTh5kUTm5Ts7iZJtpqlA3wpAS2rsz83NRWhoKDZu3IiqVavC1tYWPXr00NmwHdv58OED9u3bp/K0gDqkpaXB29sbQUFB6NChAyvm5lSFxb+e0klR4eTqIq/munTpIlNzytCHIZ1v375h48aNCAsLo6Q9Os/58+fPcHZ2xoULFzBgwADK1ZwiK1euxJIlS1TKH8joHJ5zFoosbMADIMwCtlbXqovIyEjw+Xw8evQIXbt2RcuWLREcHCyrDVeWKOoez8vLg4WFBQ4dOkSp2pKqubi4OEyfPh3h4eGMqDltftucw9MhxYWTq4JUzTk5OeHbt2+YMWOG3qo5eSQSCSwtLYsMJ2cDEokE586dg4uLC3g8HubOnQtra2va58yCg4NRvnx5jBo1quSdmSZarGw5ZD7k+3YNyM3NRUhICLy8vFCvXj2Ym5tj9erVGD9+PAIDA/XihU6XrF+/HjNmzKAkOE2q5oKDg9G+fXtYWVnpLFk8HXAOT0doE06enJwsU3Ndu3aFtbV1kWpOH7EW7kHm2pHY2jEFxngIE7RAK7Ajg/unT5/g4uIiU3N79+5VWvyYDqKiouDo6EjLsBQtGBsWr/CM1bvv5dXcuHHj4OHhASMjIxBCMHPmTGzatAm1arEzsQBTnDt3Dl+/fi2xfFZJ3Lt3D05OTvj06ZNezM2pisoVz0sDqampMDIy0qhSrrZYWlpi4sSJxUbYyUMIwe3bt8Hn82VqbuzYsRrNUbC5NpztmzPY0vwrDHkGILz/1tAJ0Rtz0ELjdrU5Z2VqbuDAgTqNgMzNzcXo0aNx5MgRlSPsMjIy0LBhQwBAXFyc7ssDReYBbeKVz+EZAHhVp8Q5vJycHISGhhZQcz169Cig4pycnJCUlIRVq1bJPmPzPU4Xiuf8+fNn2Rx+lSrqBwilpqbCx8cHwcHB6NChA8zNzVmp5hITE1G7dm16K55zaI4q4eRSFNWcjY1NsZlG9Jm7ybHY0uwLYGAAsWwsLP9fU9xEX/yIltBuzkcdmFRzitja2moUTs7o8F6rcvnRmKYKUZoE+Z8X4+wU1VxRddqePHmCU6dOISgoiK6z0Euky3n279+vlrMjhMjm5qRqLjw8XO+nSYqCc3g0o0o4uVTNOTk5ISEhATNmzMCJEydKdcQZIQSzLgpgOLYVlM3s8MCDEG+wFV1otUOq5pydnWFgYAATExOdzM0Vx4kTJ5CdnU1rODltzKmSH40plFuHZ1pZqbNTVHMWFhbYvn17kU47PT0dy5cvh4+PDzvWG7KIrVu3YuzYsWjXrp1K+0sLOYeEhKBjx474559/WKnmqIZzeDRSUjh5cnIyPD09ERYWhm7dumH16tWlVs0pcuDAAVQe0gSkCEFCAEQjnbb+4+Li4OLigosXL2LgwIHYt28fY2pOng8fPmDv3r0az9uxYoaiZbliozFfv34NPp+PJ0+eFKvmFFm6dCnWrl2LH3/8kUpr9Z4rV64gMjIStra2xe5HCJHNzUmHP0uzmlMG5/BoRFk4OSEEt27dAp/PLzNqTpF79+7h2rVrGLzYGk/wAsorHQDGoDZiUyKR4OzZs3BxcZGpORsbG9aohby8PFhaWmoVTs7WiMWcnByEhITA29sb9evXh7m5ORwcHFS2183NDU2aNMFff/1Fr6F6xrdv37B+/XqEhYUV+V0qqjl9SC9IF5zDownFcHIm1Rwr3vq/k5KSgpUrVyIwMBAJvHLYgQil++VXOtD8+5E/Z7aqOUXs7e3x999/a/UwYpvD01TNyfPy5UsEBgYiNDS0yH3YdI/rCrFYjPnz52P37t2oXr2gopaqOT6fj8+fP5equTkutRjLkIaTh4eH4+bNm2VazclDCMHChQtl4eS1AAjRG6a4+T06UxrjkB+lqU3Ailgsxvnz5+Hh4cFKNafI+fPn8eXLF2zcuJFpU7RGqua8vLzQoEEDtdWcPFlZWVi0aBHc3d256hAK7N27FwMGDEDnzp1lnymquRUrVpRZNacMzuFRTG5uLszNzdG3b1+MHDkS3bt3h62tLVq00DzEvrTA5/PRoUMH9OnTR/bZHLRAX/wIId4gGukwRjWYoqXGzk6q5qSRlvv370e9evWoOgVa+Pz5M7Zt26bzPJmiSCDDGRBHA4bGQFUToLwWyztfv34NJycnPH36FOPHj4eXl5fWy3+srKzw77//ypZbcORz69YtPHjwAB4eHgXm5qSlv0qLmqMcUoZISUkhAEhKSgrlbUskEnLjxg3Svn170r17dxIQEEBycnIo70cTRCIREYlEjNrw+PFjMnbsWCIWiylvOy8vj5w8eZJMmjSJTJs2jZw7d47k5OQwfs6qkJeXR0aPHk2ePXumdVvp6enEyMiIGBkZkfT09GL3TXMmJMaAkBjDgv+mu6jXZ3Z2NvH29iYjR44k5ubm5O7du0QikWh+EnL4+voSa2trlfZlwz2uKxITE0m/fv3I27dvyYEDB8igQYPIv//+S169esW0aTohISFB4+c4t/BcS5KTk+Hh4YHw8HDUrFkTlSpVgoeHByVtUwXTi3LT09MxZswY+Pj4UBphFxcXB2dnZ1y6dAmDBg3CnDlzZGqO6XNWlc2bN6NBgwYwMTHRuq2MjAz89NNPAICPHz8WufBcFAl8boMiF4jXfwWUL2H6VFHNTZs2jdJkDm/fvsXixYsRFhaG8uXLl7i/vlxvbZFIJBgyZAiqVKkCiUSCadOmYcKECWVKzXELz3UMIUQ2N5eUlIQZM2bA0dERlpaW+pMGSodQGU4uFotlkZblypWDiYkJVq9ezdq5ueK4evUqXr9+jdWrV1PWpirvrxnOKDYFWIYQqLm18KacnBwEBwfD29sbDRo0gIWFBXbu3KmVvcrIycnB/PnzIRAIVHJ2ZYGUlBR4e3vLAq527NiB5s2bAyj9Tp5KuG9KDZKSkmSLyLt37441a9agRYsWyMvLw5gxYyjPTl4aoCqcXFHNHThwgPVzc8URHx+P9evXIzQ0lNLISlXaEkej2CTP4uiCH7169Qp8Pl+m5ry9vQtFBVLJypUrsWjRIjRp0oS2PvQBQgju3r0LPp+PL1++oE+fPmjbti2CgoLA4/FkqpZDdTiHVwKKam7mzJmFIi2pCCcvLUQiF85IQTREqBafijfXL+H8EYFGbZUmNSePRCLBvHnzsGvXLlodR1EYGqNYhWdoXFDNNWzYkDY1p0hoaCgMDAwwevRo2vtiK1I1Jy3kvHLlStSrVw9jx45FQEAA65ae6BOcwysCeTXXo0cPrF27VjaEIE9pCifXFhekwAyf85cWEEDygwQGjtbw4KVjDlSvQF3a1Jwie/bsQf/+/QuEk1OFKkOaVU2ANIeij9//ZSuuj76sEzUnz/v373H48GEcP35cJ/2xCaJQyHnGjBmySEtCCGbPno0NGzagdu3aTJuq13AOTw5lau7kyZNFziMwFU7ORiKRCzN8/i8OggfA0BASAKb4jL6ojJYoev2hvJorX758qVFzity+fRv379+Hl5cXLe2r8vZfvhVQSwgkmgLStxMCAiIBjv/ujhELh2BdN+rmFVVBJBLB0tISR44cKVPrVFUp5CwUCtGmTRv07duXIStLD5zDg+pqTh6xWAxLS0vs27dPo1IcpQ1npBRf7Bop2Iq6hbZ9/PgRzs7OuHz5MgYPHoyDBw+W2lyJSUlJsLGxQXBwMOPDUlXnAB8avMXztdGQxBqgTuea6Ly1FRZ2nsOIPWvWrIGJiUmZWK8qr+a+ffuGv//+G8ePH1fq6J89e4Zjx45pXDSaoyBl1uGpq+YU2bZtG8aMGaNydnIm0cXKk2iIii92DZHsb7FYjDNnzsDV1VWm5mxtbSlVc2xbbUMIwfz587Ft2zbUrFmTtn5KcqTZ2dkIDg6Gj49P/tzcEQt069aNNntU4dSpU0hLS8PkyZM1boNt11sZqqg5eTIyMrB06VJ4e3sr/W3owznTgTbnXSYd3tGjR3H+/HmV1ZwidIST6zvGKA+eNDeYArzv28uSmlPk8OHD6NmzJ3r27MlI/y9fvgSfz8fz5891PjdXHB8/fsSuXbtK7XIeqZpzcnJCfHw8ZsyYUaSaU2Tp0qVYvXp1qZq/poLbt29rfGyZdHgNGzbEiRMnNFrjQ1c4OZ3owk4TGGE7iQfAA+T7I4AEBI+WrMG/CWkwNTWlXM0pg03X5uHDh7h48SICAgJo70v+7Veq5ry9vdGoUSOYm5szrubkkVaHOHjwICpXrqxVW2y63kC+mvP09NS4kLOHhwcaNmyIAQMGFLkP285ZFyQkJGDrViWLRFVFuyQv+oW2qcXEYjGZMGECefjwIbWG0Ywu0i6FhISQQV5HiAF5SQzJS2IgeUl44giCvAgy+YQP+fLlC639K8KWVFOpqamkX79+JD4+nva+pKnFqlWrRhYtWkSGDBlCnJycSGpqKu19a8K6deuIu7s7JW2x4XpLJBJy8+ZNYmJiQkaPHk38/f01Si/48uVLMmLEiBLPhw3nrEskEgmZOHEi+d///qfxc7xMKjxN2b17N23h5PqMNJw8LCwMnhevYldyNLLr1Uafhk2xvkl7tB7+C9MmMgL5Xh1C03Dy9Egg1hnIigYqGwONTYBqRUz5ZGdnw8/PDxkZGeDxeJgyZQqro/ouXLiADx8+wN7enmlTtCY5ORleXl4ICwvTSM3JI60O4erqymVQUWDv3r34888/tXr+ct+oity6dQv379+Ht7c306awCpFIhNmzZ6Nz584YNWoUhgwZgiuzZ5eZubnicHZ21jicPNYFeGyWPzpMSP6/bx2ATkKg8Zz/9nvx4gX4fD4iIiIwcuRIVKlSBTweD126dKHuRCjmy5cv2Lx5s14v5yGE4Pbt2+Dz+WrPzRXHihUrYGVlJcuJypHPnTt3cPv2bfj4+CAhIUHjdjiHpwJJSUlYvXo1K8LJ2YJYLMbp06dhZWWFunXrYvTo0di9e3epWzenKdJw8uDgYLWPTY/Md3aQ/JcBTPrvY1Ogao8cnHoUCB8fHzRq1AgWFhbo2rUrMjIysGbNGqpOgRYkEgksLCywd+/eIpNbsxlFNbd69WrKllIEBASgWrVqGDZsGCXtlRaSk5NhbW2NgwcPYsuWLThz5ozGbXEOrwSIjsLJ9YUPHz7A2dkZV65cQdOmTdGnTx+4uLgwbRarKCmcvCRinb8rOyXbJESMA6NC0dAmE76+vqhWrVqB7YTloerbt2/HyJEj0aFDB6ZNURl5NSct5EyFmpPn3bt3cHZ21mvVSwd5eXkYN24cDA0NsXHjRpiYmMDS0hJ16xZe06sKnMMrgUOHDjEaTs4GpGruwMnTiP1zEOrNtETbecvw4J/F+J/TUabNYx3Lli3TKpw8Kzp/GFMZBjwDjPp1CrqaK9/O5hGIa9euISIiAu7u7kybohLJycmyhBTdunWjVM3Jk5ubi/nz58PJyYmrDvEdaXpBT09PNG/eHC4uLrLfU2Jiosbtcg6vGB48eIBLly7pJJycjXz48AFCoRBXr15F7SUrcG7zfvB4PLwEwSWxBLwDrvAz5GEO04ayCE9PzxLDyUuisjFQ1KJGHo+Xv13PSEhIwLp161i/nIcQglu3boHP5yMxMZEWNaeItbU15s+fj6ZNm9LWhz6gmCz+jz/+QNu2bREYGEjZVAnn8IogNTUVK1asKBXZydUZ5hKLxTh16hRcXV1RqVIlmJqaYprtOvySwZOrF8oDDA1BAJhmAX0NgZaGNBiuBUwM7b1+/Rp+fn4IDQ3V6Pjs7GwEBgbi1K0rmCo5+t3dFbz3CAGamBbdBhvvVUIILC0tsXPnTkqLxCr2oQ2Kas7W1lYnac7Cw8MhFosxduxYtY9l+/C1qihLFl+lShWMHTsWfn5+hZydNufNOTwlEEKwaNGiMpWdPDY2Fs7Ozrh69SqGDh2KI0eOyMbJbbKLrSYDoQjYyjKHp2uys7OxaNEiuLi4wNBQvS8jIiICfD4fL168wMSJE+F4bDeSAg3w2LRglCYh+VGaVTWLeGcMaTh5165dmTalAIpqbubMmbSrOXliYmJw8ODBUptlpjgU1ZypqaksWTwhBHPnzoWdnR3q1KlDab+cw1NCWclOrkzNrVu3rpBKiJYoD6AAvufJlBSxsQyxYsUKLF++XOVw8qysLAQFBcHHxwdNmjSBhYVFgaUE1eYAtfoCMcL/1uE1MdU/Z3fnzh3cunULvr6+TJsiQ6rmwsLCZIWc1U0vqC0ikQjz5s3D4cOHUbFiRZ32zSRxcXEQCoWy9ILKSn+5urqiZcuW+OOPPyjvn3N4CpTG7OSKDiw2NhZCoRDXrl3DsGHDCqg5ZRgbADwUMaf0fTvb0OXQXkBAAKpWrapSOHlERAScnJzw8uVLTJo0CX5+foUiLaVUbQn8omYWJTYNc0nDyaUVuumkpPaVqTnFQs66xM7ODrNmzdJ4gTrAzuFrZaiTLD4iIgIhISHFPn+1OW/O4cmhbTg5m8nLy8OpU6fg5uaGSpUqwczMDHZ2dirdPCblge1ZJN+7KexPAJiW4cCyR/+LwdlVEgzssRXnbICuJkBthWwoWVlZCAwMhK+vL5o2bQpzc3PaFoazxeERQrBgwQJs2bIFP/zwA2N2KJb+YkLNKXLmzBkkJiZi6tSpjNpBN+omi8/MzMSSJUvg6emp9rSAqnAOT47SmJ08NjYWfD4f169fx/Dhw0tUc8r4cvMaej2KwO2Z5vn1QgHZv8LK7AtY0RV3+Xk4ZtEIPxlOxov3PIAHXHcAxgiBLnP+U3OvXr3CxIkTi1VzVMGWt/6jR4+iS5cu6NWrl877JlqW/qKTT58+YceOHaV23k6b0l/Lly+HtbU16tevT5t9nMP7jirZyfUFeTVXuXJlzJkzB2vXrtXoBy8NJz8dGoqvVXkQivLn7IwN8pVdWXV2CZHAMUsD8GAAIpbfQhBqAmx0NUf9thVgYWFR5nKvPnr0COfOnUNgYKBO+01KSoKvr69ahZx1iVgshoWFBQ4cOKB1dQi2oW3pL29vb9StWxcDBw6k0UrO4QEAXr16BV9fX4SFhTFtilYozs0dPXoUderUQV5enkbtKYaT1wAXjSnF3yYSgLKHKQ/gSWDW7TCG79L9/BDTQ5ppaWmwsrJSGk5OB1I15+joiOTkZMyaNYs1ak6RTZs2YeLEifjll9KRTF2akMLV1RUVKlTQuPRXZGSkLF0b3ZR5h5eVlYWFCxfCzc1NL7OTS9Wcq6srqlSpotbcXEnYHnZFykRr7CjfFcZvAJOGQKsqFBit58TExODZtQ+oy2upNCMKDwbIiGMmGILJIU1CCBYvXgw7OzuNUz+pSlJSEjw8PHDs2DH07NkTtra2aN68OWt/wxcvXkR0dDTs7OyYNkVrPn78CKFQiCtXrmDIkCE4dOiQxsnis7OzsWDBAtnyBLph592hQ/Q1O3lMTAyEQqFsbs7R0ZHSNStrr73D1lazYWjIA/mSH6viEA0I2wJzGlLWjd4hEokwY8YMdKm7EpKvEvCgRPLygJrGOjeNcVxdXdGiRQv8+eeftLRPCMGNGzfA5/ORkpJSYG5O01EMXfD161ds3LhRr/NkKlNza9as0VrFr1y5EsuWLUOjRo0osrR4yrTDk4aTDx8+nGlTVCIvLw8nT56Em5sbqlatClNTU6xfv57yt/r7n1OxKbMpYGAAsUK6ftMIoG9NoGUZU3pZWVkICAjAhg0b0KxZM0za1Bznxxsqz3lJgK7FZEMpjagSTq4pimrOzs4OzZo1o7wfOpBIJLC0tMTevXtpD1iiA/lk8dqqOUWCg4NRoUIFjBgxgpL2VKHMOrx3795BKBTqRbSUtmpOnXkdQghmel2EYafRECvZzgMgjAO2snwBNFVzWc+fP4eTkxNev36NX375BX/++SeEQiEAoKoQCDMFFENXxwiB2gx9P0wMaWZmZmLx4sWUhpNL1ZxAIEBycnKJkZZMz10WxY4dOzB06FB07NiR8rbpOme61Jw8UVFRcHJy0kj1cqnF1ESandzR0ZGVk9tAQTUnnZujQ80pcvToUVRs8hdIEcnECIDoLFpNoI2PkcBZZ+BrNPCjMTDYBPhJSQVxqZrz8/ODsbExLCws8OOPP2LmzJkFXpC6zAGa9AUeCIHk6PxhzK6mzDk7ppCGkzdo0EDrthTV3Lp16/RGzSly48YNPH36FB4eHkybohLSZPFXrlzB0KFDcfjwYVrmYqXP3yNHjuh84X+ZdHh2dnaYN28ejI2NmTalEDExMRAIBLhx4wZGjBhB+dxccTx69Ajnz5/HkG3z8DQGSvOJ8QAY62FE9VkXYJ9CBfFAB2CZEBg0J3+fZ8+ewcnJCZGRkZg8eTL8/f1RtWpVWXJfZeHktVsCg9TMhlKakIaTDxo0SOM2FOfm2BxpqSqJiYlYs2YNQkJCWLM2Uhnyaq5ixYpFphekEltbW5ibmzPyIqM3Dm/z5s04ceIEHj16hAoVKiA5OVnjtsRiMcaNG0edcVqSl5eHEydOwM3NDdWqVYOZmRns7e0pu+lUaSctLQ3//PMP/Pz8kFSFhx3vle9HAJjqQdCK/Dl/jMx3dkRJBfG9pgSvvobg5CUBmjVrBgsLC3Tq1KlAW5s3b9abcHKJRHeJTbUNJ09KSoK7uzuOHz+OX3/9Vau5OTY5FUII5s2bBwcHBxgZGdHWjzbnLF/6i041p8iJEyeQnZ2NCRMmaNxGmUgtlpubi0mTJqF3796yORRN2bhxI0VWacf79+8hFAplao7P5zNSnUE+nLxOnTqog/xoTNOIfCUkyQLwDSC5wNCGAMkGoEdBK2eLqSBOiATvLreUBTApcunSJURHR2PdunX0G0oBunrwaxpOTgjB9evXIRAIkJqayqosKFSxf/9+/Pbbb+jevTvTphRA1WTxdPHhwwfs3buX0bgJvXF49vb2APJDn7WFyezkdKs5TVCWnXxOw/xozKXXgZNP8x2GAYAzSUCb54BwODCH+nl4WvgaXVwFcUPUq9ERSnwdvn37ho0bN+p9QgI6UDecPDExER4eHpSoOTZz7949XL9+HX5+fkybIqO40l+6Ii8vD5aWljh8+DAqVaqk077l0RuHpwk5OTnIycmR/Z2amgogfy2VSCRSKcO6lOL2VWW/9+/fw9nZGbdu3cKwYcNw+PBh2dycWKwsHvK/drW1U36NkuK+ERERCA4ORmBgYKH9ctOB0/fLAeCBEHmFRGB6EujVQIyWP6j+PWl6TlFvePBxNUDse6BxU2DaHAmat1K+r7TdAuuyKieAkDqA0jVzBHWaEOTlFRwKFIvFMDc3h4ODAypVqlTsOi+qrpMm+8rvl5eXh+rVq8vsV7SZqusUEhKCcuXKYciQIRCJREW2KVVzzs7OSEtLw/Tp0xEWFoby5cuDx+MV+Z1qYmdRvyFVz0nb/oH858u///4LPz+/QvbQce2l3x8hpNB+0rk5d3d3VKxYESYmJrCxsQGPxyv2u1enf3XOae3atZg6dSqMjY1LXDNZ0nXSZs1lqXZ4W7dulSlDJpCqOU9PT1SrVg2mpqaUZUGhgszMTCxfvhxubm5Kw8ldnxoUEavJAw8ELk8NsPkPeueMfN14+MfSsECwyaGdhtjtJMHU2UWHJ2dmZiI4OBhBQUFo9ENP8Hjrv/+Q5M+IgBBg0NzC57B7924MHjyYlnByOqH73oqKioJAICh2vV1iYiI8PT1x8uRJWaSlsbExa5cOUIG0aLS9vT1q1arFmB2xsbFwcXHB9evXMXToUBw8eBB169Zl9Ls/f/484uPjWVEdglGHt379+hId0t27dzUeC7exsYGVlZXs79TUVDRu3Bjly5endc7g/fv3EAgEuHnzJkaOHAmBQMCKyumKcy2LFi2CjY1NkcNSsWnFFX7l4flHHtYGGCD6G2BcFzD5C2ilfWS6jLeRwD+WgLI4DCsLQ/T5E2iusATg6dOncHJywps3bzBx4kQEBgaiatWqODcY2Pu9grh0zRwhPCwTAk3aFPxebty4gefPn8PDw4M1LyeqUK5cOdkohqGhIeWpmnJzc7F48WIcPXoUVaoUnMQlhODatWsQCARIS0vDrFmzcOrUKZ3NzUmvE1OpxRwdHdG5c2daipaqgmLpL6anSaR8/vwZO3fuRHh4OGX3gjbXmFGHt2jRohK9vjZLBypWrKiz+TqRSIQTJ07A3d0d1atXh5mZGTZs2MCKm04ZqmQnN66prORrPiQBOPkYOC2nvBzCAaElMOevwvtHRgHOgUD0B8C4EWAyEWhVwhSOt3Oh8nsyeDzASwis3Zqv5vz9/eHv748WLVrA3Nwcbdu2BfDfj2PQHKBdX+CM8L91eENMgYYKDlNfwsmLgs43eWXh5ImJibJIy969e8Pe3p6Vy33o5MmTJzh9+jSCgoJ02q9Uzd24cUOlQs66RlodYv/+/YVekJiCUYdXp04dna0xo4vo6GgIBALcunULI0eOZCzSsjgUH4KvX79WKZzcpCPgcEvJhhyAxOb/30KpxxyBvm2AlnIlrVwCATObgmvgHJwA4VZgzsSi+4+JLjrYhBDg6aNkLF68Fm/fvsXkyZMRGBgo+2HJzy1JadgSmFvMmjldhZPTCV0VCuTDyZlWc8pgasguPT0dy5Ytg6+vr06qQ8iX/qpYsSLmzp3LGjWnyNatWzFu3DjZyydVlIlMKzExMUhMTERMTAzEYjEePXoEAGjZsqXOc9SJRCIcP34c7u7uqFGjBszMzLBx40ZW3nSKZGdnY+HChSqFk7eqlR+NaXqyYPYscSJgwAMkyham8wDhRWDrtPy/I6PynZ2yYUlTG6Bvd6ClsfL+mxgXrfAkRIxPX+9grYMFOnToUOx5qMqBAwdYGU7ONNJwcjc3N+zdu7dMqzlFlixZgnXr1lGWX7IolJX+kr6UsfG5c+XKFbx58wa2trZMm1IAvXF469atg5ubm+zvLl26AMgvu/HXX3/pxAapmrt9+zZGjhwJoVDI6AS1Jvz7779qhZPP6Qj0bQQInwDRyfnDnE/vAae+Kd+fECBabptzYPHDksIAYOu/yrdPNwEOOCjtBQY8A7j5DS40h6cp9+7dw7Vr11gVTs4GRCIRJk2ahPr162Px4sWYNWsWTp8+zdoyPLrEzc0NTZs2pe35U1LpL2WjGGzg27dvsLe3R2hoKOucsd7cta6urpSswVMXRTVnbm6uN2pOitTWoKAgVKxYUe3s5C1rAVv/+u9vm0/A6QdQnnqMlx/AIiX6Q/HDktEfiu63wU+ZmDjnPvydfwOPR8DjGYDH44EQHvYJCwesFLRD9euTkpKClStXIjAwUK+uqzKoGtpLSEiAu7s79u/fj06dOmHv3r1o2rQpJW3Tga6v24sXLxAYGIjQ0FDK21Y1WTwb71WJRIJ58+Zh165dsiUyVFMmMq3omtKg5uSRZienIsuByV/5ASrKIAQw7fff38aNild4xkqE5pMnT+Dk5ISoqChMnjwZi5Z1R5B3ZcRE5w9z/m1avLNTB0IIFi5ciE2bNun19aUCQgiuXr0KgUCAjIwMdOrUCQMGDIBAIGDaNFaR9f/2zjusqfN947f6c9WBWlvrXriqtdbVam0VtY46q2Kx4qgKooDgQgQV3LO4Bwkb2Vtxt65a6yoiDrTiAAEVBAXZgZzfH36TxhhCxpnJ+7kurquN57znOclJnnO/732ep7gYdnZ2CAwMpK07BFutv5jGw8MDw4cPR69evbgORSUk4SmgqOZMTEwEtTanjrKyMtja2sLT05OW6uSdmr9zY871fN+IQlHvXlc0rMyZ8s6gogqKAuaav/vvwsJCudOyU6dOmD9//ntrc58zVKBZLBbjiy++wMCBA5k5gACQqbljx45h4MCBWL9+PWrXro3p06cLon0W2yxevBhOTk5o0UL/orJMN3JmkytXriAhIQFBQUFch1IpJOHhv4dpr169inHjxglezSmzatUqzJs3j9ZSTrOHvHNjep+D/Dm8uWbvJzvg3aMH3pvfGVQ+SI6bgaL8JNjZifD48WP8/PPPiIqKYs3CnJSUhBMnTrBuJ2cSTac0ldWc4tqcrLg6n+zkfCE0NBSNGzfGyJEjdR7DUNScIq9fv4aLiwuio6N5fR5Gm/AkEgmOHj2KgIAANGrUCFZWVtiwYQOvPyxdiI+PR2lpKSZNmkT72Kaf/efGVMfsKe/cmN4R79bsWjYrQ9PaRxDm7Y2bnTvDxsYGPXr0oD0+dRQUFGDx4sUICQlhxU7OFlVdv6rUnPLa3ObNmzFx4kR0796dyVAFR0pKCvz9/XVqWgr8p+YuX74seDWnCEVRWLBgAbZu3YpGjRpxHY5ajDLhrVu3Drdu3cK4cePg4+NjUGpOkfT0dOzevVttGSi2MG0HWIy4BZFIhOS/nrKu5pRxcHDA6tWrGbeT8wGKonDx4kV4eXmhqKgIs2bNqtRpefHiRTx8+JB3dnKuKS0txcKFC+Hl5aXV84bKao6tRs5ssn//fnz99dfo168f16FUiVEmvBEjRmD79u0GddEpU15eDmtra+zfv5/T6uSFhYUICwtDREQEOnfujAULFrCu5pTx9/dHmzZtWHuchU0UpzRzcnLg7++P48eP49tvv8XGjRvRpk2bSvfNzs6Gu7s74uLiDPq7oQtOTk6ws7NT+/4potzIWSQS8a4gBR0kJCTgwoULCA8P5zoUjTDKhPfNN98Y/Bfa3d0dlpaW6Ny5s17VxXXl1q13au7p03dqLjo6+oNu4Vxw//59REVF8UL1MkVFRQXmzZuHsrIytWpOEalUivnz58PDw4MxO7lQiY2NRfXq1TF+/Hi128mKxQcEBMjVHF+roNBBfn4+li1bhoiICMGco1EmPEPnzJkzyMrKwoYNGwCwV3ZJWc0tXLiQs3UgVedcXFwMe3t7BAQE0GYn5wuvXr2ST1nWqFEDbm5u6Nq1q8b7891OXhVMXeOpqak4cOAA4uPj1W6j2MiZLTXHZQcEWXeIdevWsa5cjaK0GEEzXrx4gS1btrBqJ7916xY8PT2RmpoKCwsL3qg5ZZYsWYLly5ejeXMaWzpwiOLaXHFxMX7++WfUq1cP1apVQ+vWrTUe58qVK/jnn38QHBzMYLTCQyKRYP78+Th48OAHj/PwsZEzm3h7e6Nbt24YNGgQ68cuKirSeV+S8AwINquTFxQUyNVc165dYWtry2tXX1hYGBo3bowRI0ZwHYrevHr1Cv7+/jhx4sR7a3OFhYVa/+AKxU7OBatWrcKcOXPQsWNH+WuKrb/GjBnDy2LxTHPnzh3Ex8cjOjqa9eOKRCIkJyfrPAZJeAZEZXZyOn/IEhMTIRKJ5GouJiaGl2pO8ZwfPXqkl52cD1AUhQsXLsDb2xvFxcWYNWsWHBwcPlib02a6R2Yn37JlC+/t5FVBd7I+ceIECgoKMHXqVJSXl8sLUvCp9RcXxy8sLISDgwOCg4NZeZynqKgIERERCAsLk7f+atWqlc43GSThGQhM2smFpuYUUbSTC7HgsaKaGzRoUJVOS23Yv38/+vfvj/79+9MynqGQkZEBDw8P7Nu3D6tXr5Y3cjZGNaeMg4MDXF1d0axZM0aPI2vkrKr1V25urs7jCu8XgPABTNnJExMT4enpibS0NF6rOXWsWLECdnZ2Wq1pcY2maq6yfTUhISEB58+fR0REhL7hGhTFxcWYMGECGjdujE2bNvFGzfGBwMBAtGzZEkOHDmVkfOVGztbW9LX+kkESnsCh205eUFCA0NBQREZGolu3brC3t6e9gSNbxMXFoXr16hg3bhzXoWiEsprbtGmT1olakx9mIdrJmebp06fw9vZGUFAQBgwYgL179xpsQQpdePDgAcLCwqpsGq0L6tQc3ZCEJ3DospPfvHkTIpEIaWlpmDZtmiDVnCKpqanw9PRUayfnAxRF4fz58/D29kZJSQlmz56tsZrT9Xhc2cn5hkQikT8316BBA/Tu3RtmZmbw9vbmOjReUVxcDFtbW/j7+9P2OA8bak4VJOEJGH3t5Iak5hSRSCSwtbXFvn37aOkOwQSvXr2Cn58fTp48ie+++w6bN2+mZdq1qilNb29vdO3alRM7OV9Qbv3l5eUFiUSCX375RdDGJqZYunQpli5dipYtW+o9lqKa+/nnnxlVc6ogCU+g6GMnl6m5Z8+ewcLCArGxsZyWH6ObVatWYfbs2ejQoQPXobyHoporLS3FrFmz4OjoSKuaU3ct3LlzB0ePHjXoKjOVoa71l1QqxaRJk7B7927Uq1eP61B5RXh4OBo0aIDRo0frPIaimjM1NWVNzamCJDwBooudvKCgAJGRkXI1t2jRInTr1o3ZQDlAZiefMmUK16HIyc7Ohr+/P+1qThvYtpPzBU0aOW/duhVjx47lvMYr33j06BF8fHx0LmJx+/ZteHp6yhs5s63mVEESngDRxk5+8+ZNHDp0COnp6fjll18MTs0pIrOTHz16lNOyS4DqtbnFixczXtKsMoXn4OAAFxcXxu3kXKH4eWvTyPnSpUtITk6Gs7Mzm+HSApPXeGlpKRYsWACxWKxVd4iqGjnTASktZkRoYid/+/YtQkNDERUVhc8//xy2trbo1q2bVheu0CgvL8f8+fOxb98+1KlTBxKJhJM4srOz5Wtz33//PbZs2YJWrVpxEouMwMBAtGjRAsOGDeM0DqZ5+vQp/Pz8NG7knJOTgzVr1iA2Npa4VZVwdnbGwoULP+iVWBlJSUkQibhp5KwNJOEJiKrs5AkJCRCJREhPT8e0adPkao6Lbglss379elhYWKBLly4A2K1CQVEUzp07B29vb5SVlWH27NlYsmQJJwWqle9+Hzx4gNDQUEbs5HxAsZGziYkJrK2tNWrkTFEUbGxssGPHDjRs2JClaOmFqWv8yJEjkEqlmDhxotrtlNUcW42c9TlvkvAEQmV2cpmai4yMRPfu3eHo6KhVlXxD4OzZs8jIyMDatWtZPW5WVhb8/f1x6tQpfP/999i6dSvnak4RRTu5EKvMqOPJkyfw8vLCtWvXMG7cOIhEIjRp0kTj89y1axcGDx6M3r17MxypsEhLS8O+ffvUrtslJSXB09NT3vqLr2pOFYb1LTBglO3kimrul19+QVxcnMGuzanj5cuX2LhxI2t2cqlUKl+b41rNqUJR4S1btgxLliyhxU7OB2RqLjAwEI0aNcK8efPkak6bWYxr167h6tWrCAkJYTBa4SHrDnHgwAHUrl37vX/jYyNnXSAJTwDI7OQBAQEQiUSIiopCjx49jFLNKSKrMsOGnZzvak6GbLonOjoa9erVw48//shxRPqjrOZ8fHzQuHFjncZ68+YNnJ2dERUVRdbtlFizZg1mzZoFU1NT+WvKjZyFpOZUQRIezyksLMScOXPQpUsXWFpaYtq0aUar5pRh2k4ulUrla3MSiQS//vorr9RcZUilUgQGBuLYsWNch6IzimtzjRs3hpWVlUZrc+qgKAoLFy7Epk2bdE6YhsqpU6fw+vVrWFhYGIyaUwVJeDzl7du3CAkJwbp16zBgwAC4uroatZpThkk7eVZWFvz8/HD69GkMHjwY27dvF8y0oFQqRVFREXbv3i1IV+6TJ08gFotx/fp1jB8/Hr6+vrQlp0OHDqF379745ptvaBnPUMjMzMS2bduwadMm2NraytUcXxs560M1iusHllgkPz8fJiYmyMvL460z659//oFIJEJmZiZat26Nxo0bY+PGjXqNKVvfMBTjQk5ODszNzREbG1vp56jtOcvUnI+PDyQSCWbPno2RI0fyXs0pUlhYKDduZGVlCaZqiEQiwZEjRxAYGChXcwMGDNBKzVX1eScmJmL9+vWIiIgwmAfv6fhe5+fn4/vvv5fXErW2tuZ966/c3Fx8/PHHOv2OG8YvoMCRqTnZ2tySJUsAvKtht3fvXo6j4xd028mV1dy2bdsEo+aUkU1hCkXZPX78GF5eXoyoOUXevn2LpUuXIiwszGCSnb7cunULnp6e+P333zF48GDs2bPH4NScKkjC4xBFNafotCwuLsb48ePh5+dHi8IwJBGvqZ1c3Tkrrs2Vl5dj9uzZWLp0qaDUnDJpaWnw9PRE3bp1eW3GUKXmNm7cqHfMlX3eFEXB3t4ebm5uaNq0qV7H4Bvafq+VGzn369cPxcXFEIvFDEXIDKTSioB4+/YtgoODER0djS+++AJLliyRPywtw9Ds5HShr508KysLvr6+OH36NIYMGSKotTl1SCQS2NjYYOfOnRg8eDDX4ajk8ePHEIvFuHHjBqNqThk/Pz+Ympri+++/Z/xYfCUxMREikQipqanyRs5v376FhYWF0XWHIAmPJW7cuAGRSITnz5/L25AoP+sCABEREahfv75e1ckNEV3t5FKpFGfPnoWPjw8qKiowe/ZsLFu2TNBqThk3NzfMnDkTHTt25DqU95BIJIiLi8Phw4fRpEkTWFlZYdOmTawp0Hv37iEmJsYou0MoqzlbW1v52pxUKsUvv/yCXbt2oX79+hxHyi4k4TFIfn4+QkJC5Gpu6dKlH6g5RR4/fgwfHx/a77r4PMWlCbrYybOyshAQEIA//vjDoNScMqdOnUJubq7cTs6H6etHjx7By8sLN27cwIQJE+Dn56dxVw9dUb7Gi4qKsGjRIhw+fNigbm4UUfW9TkxMhKenJ9LS0uRqTnltbvv27Rg1ahR69uzJVqi0QkqL8QiKouRrc8+fP8f06dMrVXOKlJWVYcGCBRCJRIIxHbCFpnZyRTVXXl6OmTNnwsnJyWB/8J4/f47t27e/VwaKq4RXVlaGI0eOcKbmlFm8eDGcnZ3x2WefcXJ8NtGmkfPly5dx+/ZtBAYGshwlPyAJjyYU1VzPnj2xbNkydO7cWeP9nZ2dsWDBAo2rkxsLiYmJ+P3339V2h3j58iX8/Pxw5swZDBkyBDt27MCnn34KAAab7CoqKmBtbY29e/e+dwfPdoLhQs1VRXBwMD755BMMHz6c0ziY5ubNm/Dy8pIXi1el5hTJzc3FqlWrEBMTI/hZH10hCU8PKIrCjRs3IBaL8eLFC7Vrc+o4cuQIKioqqqxObmyos5NLpVL88ccf8PHxgVQqxa+//vre2pyhd4jYuHEjpkyZwkkTX5maCwwMRNOmTTlXc4o8fPgQQUFBBtsdQlHNdenSBba2thpNTcoe59m2bRtMTExYiJSfkISnA/n5+QgODkZMTIxOak4RTaqTGyOV2clfvnwJX19f/P777zAzM8Nvv/2GFi1acBgp+5w/fx5Pnz7FmjVrPvg3Jqc0Hz16BLFYjH/++QcTJ06Ev78/52pOkZKSEixcuBC+vr4GU2RBxs2bNyESifDs2TN56y9tznHPnj349ttv0bdvXwaj5D+GdVUwiLKa03RtTh0yO7mq6uTGjqKdXJWaW758ucFOV6ojKysL69atq9TYRLfKKisrkzstZWpu8+bNvFBzyjg7O8PR0ZGXRb11QXltbtGiRe8pek1nMW7cuIG//voLYWFhTIUqGEjCqwI61ZwyMju5YnVywn928oMHD2LLli1GreYUkXWHYMNOnpKSAi8vLyQkJGDChAm8U3PKxMTEoFatWhgzZgzXoeiNKjWna7H4vLw8ODk5ITIykpc3KWxDEp4KZGpOJBLh5cuXtKg5ZRTt5IT/KCgogKWlJdq0aYMlS5YYtZpThmk7uZDUnCKy9kFCft5O1sg5KioKn3/++QdqThdkj/Ns2LABTZo0oSlSYUMSngL5+fkICgpCTEwMevXqheXLl9Om5hRRZSdnEj48m1UVL168gJ+fH/bu3YsRI0Zg06ZNaN68uc7jCeGctUFTO7kuySklJQVisRgJCQmYOHEiAgICBGNsKCsrg42NDfbu3SvIx3kUGzlrq+aqusZFIhF69uyJgQMH0hEqbyClxfSAoihcv34dYrFYruaOHj3K2JpaZXZyY0QqleL333+Hj48PAKBdu3aYPXu23t0hDA0m7ORlZWWIjY1FUFAQPvnkE1hZWWHLli28V3PKuLi4wNraGu3bt+c6FI2RqbnIyEh0796dkUbOSUlJOHnyJKKiomgdV+gYbcLLy8uTr8316tULTk5O6NSpE+PH5dJOzhdevHgBX19f/PHHHxg6dCh27tyJgoICODo6GqydXFfotpPL1NzNmzcFp+aUiY+PR2lpKSZPngyJRMJ1OFWiqOYUi8XTTUFBARYvXoyQkBDSHUIJo0x49vb2ePPmDeNqThl1dnIm4cNdu7Ka+/XXX7FixQpUr14dJSUlmDlzJq12cj6cMx1oayeXSqUfvGYoak6R9PR07N69W74swNdzUW79Raeaq+ycFy1ahDVr1siLLxgapLSYljg6OuKrr75i9ZjZ2dlYv3690SkYVWpOeW3OycnJoOzkdKGLnVzxx8CQ1Jwi5eXlsLa2xv79+xlRSHSg2Ppr2rRpjKk5Zfz9/dGuXTveds3gGqNMeGxXlZfZyXfu3GkU1cmlUinOnDkDX19fAMCcOXPkak6Z6Ohog7GT04mudnKKoiCRSDB16lQ0b94c1tbWgldzyri7u8PS0pIRQ5k+KKu5xYsX0742p47k5GRERUUJ2q3KNEaZ8Nhmx44dGDlypGCrk2vKixcv4OPjg7Nnz2LYsGEq1ZwiT548gUgkMrqeXFWhi5384cOHOHDgAAoLC1GzZk2IxWKDfGbxzJkzyMrKwoYNG7gORU5ljZzZpLi4GPb29ggMDCSP8KiBJDyGuXz5MpKSkgy2OrmimqtWrRp+/fVXODs7V7lYLusOcfDgQdSqVYulaIWBpnby0tJS+dpcs2bNYGlpCR8fH1SrVs0gpi6VefHiBbZu3cqLGyTFRs49evRQ2ciZTRYvXgwnJye9HuURCtnZ2TrvSxIegxhydfLnz5/D19dXruZ27dqlVSsWV1dXWFlZCcpOzgaa2MkfPnwIsViMxMRE/PTTTwgMDISJiQkKCwsN7jqTIXucZ8+ePfjoo484i0O5kTMXak6Z0NBQNGnSBCNGjOA0DiZRbP1VVFSk8zgk4TGEIVYnl6k5mYqYM2eORmpOmWPHjqGkpASTJ09mKFJhIns0IzQ09IP3VFnNWVlZYevWrR8kOEN74F7G5s2b8dNPP1Xa541JFNWcJo2c2SQlJQUBAQG8UL1MIGv9dfr0aZiZmWH79u2oW7cuPv74Y53GIwmPIfbu3cub6uT6/gg+f/5cvjY3fPhw7N69W+fGmunp6di1axfjVWaE+MOvyk7+8OFDiEQi3Lp1Cz/99BMOHz6Mhg0bVjqGIT53dfHiRaSkpMDV1bXSbej+vJUbOeva+otJSkpKYG9vDx8fH4PqDqFYLL6iouKD1l85OTk6j2047xKPuHHjBi5duiTo6uRSqRSnT5+Gr68vqlevjjlz5mDlypV6/aCWl5dj/vz5vLaTc4W/vz/atm2LIUOGoLS0FDExMQgODsZnn30GKysrbNu2zWCnK9WRnZ2NtWvXIjY2lpXzV2zkzDc1p8zKlSuxcOFCtG7dmutQaEHW+uvMmTMwMzPDjh070LJlS1qPIYiE9/TpU6xfvx5nz57Fixcv0KJFC1haWsLV1ZV3hgehVyfPzMyEr68vzp07p7eaU8bd3R3Tp0/nnZ2ca5KTkxEZGYlt27Zh+fLluHXrFiZNmlSlmjN0pFIpbGxs8Ntvv6FBgwaMHUexWDxdrb+YJjY2FjVq1MDYsWO5DkUvVKk5JovFCyLh3b9/H1KpFJ6enjA1NcWdO3dgZWWFwsJC7Nixg+vw5FAUBVtbW95VJ68q8VZUVMidlnSpOWXYtpML5WbjzZs3MDc3R4sWLbBz50691ZwQp3Irw8PDA8OHD0evXr2q3FaX90u59RdTxeLpJjU1FQcPHhS0GU5WLP7MmTMYOnSoVq2/9DpnSqBs27aNat++vVb75OXlUQCovLw8RmLy9PSktmzZwsjY+iCRSCiJRPLB6xkZGdSGDRuoYcOGUVu2bKFevHjByPGfP39ODR06lCosLGRkfFVUds584cGDB9SyZcuoVq1aUfb29rRckwUFBZSJiQllYmJCFRQU0BAld/z999/UtGnTKKlUqtH2mn7eUqmUunbtGmVlZUWNGzeOCgkJoUpKSvQNlzXKysqoUaNGUY8ePeL9Na5MRUUFdfr0aernn3+mzM3NqRMnTlDl5eVaj5OTk6Pz77ggFJ4q8vLyqlRRpaWlKC0tlf9/fn4+gHedxiUSSZV3CpTC3bK6bSmKQlJSEo4dO4aIiAi1nYg1HVNxW33jVIynvLwcZ86cgb+/P2rWrInZs2dj+fLlcjUn21aXOFVtW1FRASsrK3h4eKBWrVryIr90vfeVbavqM6DrnCrbtqrtSkpKEBsbi5CQEDRv3hxt27bFtGnTsGnTpg9i1ubak1FeXi6fAq2oqPjgPeDi2tNl29zcXKxcuRLh4eGoqKjQaMyqtpOtzcXFxeGLL76Ao6Pje2pOl/dem23pGtPFxQWzZs1CmzZt3vuucvE5abqdTM2dPXsWQ4YMwbZt2+RqjqKoSq/TysbUtNO7KgSZ8B49eoS9e/fit99+U7vd5s2bsXbtWsbjKSgowLJly3D48GHeuuQyMzNx+PBhXLhwQafn5nRl69atGD9+PLp37874sfjKv//+Cy8vL9y5c0de0zI7OxuOjo60l4GiBD6lSVEU7OzssGnTJr07rFP/W5vz8vJCVlYWLCwsEB0dLVjD1MmTJ1FQUIApU6ZwHUqVyNbm/Pz8QFEUZs6cKXdacjoNq7UmpBE3NzcKgNq/69evv7dPRkYGZWpqSs2dO7fK8UtKSqi8vDz537NnzxiZ0vz111+pc+fO0TomHZSXl1PHjx+npkyZQllYWFBnzpyhKioqWDv+hQsXqJkzZ2o8LUUnXE/3lJSUUMHBwdTYsWMpKysr6vr16/L3oaSkhPrhhx+o1NRUWo9pCFOae/fupTw8PLTeT/HzzsvLow4cOED98MMP1PLly6kHDx7QHSbrpKenU8OHD6eKi4vlr3F9javi+fPn1KZNm6ihQ4dSGzZsoDIzM2k/hmCnNO3s7GBhYaF2m3bt2sn/OzMzE2ZmZhgwYABEIlGV49euXZtxp5WinZwvZGZmwsfHB+fPn8cPP/yAXbt2oVmzZqw+q5OdnQ13d3fExcUJdmFdFx48eACxWIzbt29j0qRJCAoK+sBp6eTkBDs7O7Rp04ajKPlJQkICLly4gPDwcK33pf7XyNnX15eVRs5sInucZ9++fbxUp+paf/ENThNe06ZN0bRpU422zcjIgJmZGfr06SN3E3KNzE4eGxvLdSioqKiQPzf3f//3f5g7dy5cXFxQvXp1vea8dUFmJ/fw8GDUTs4XSktLER0djeDgYHmHgsrcw7GxsahevTrGjx/PSCyUQKc08/PzsWzZMkRERGh1gyRr5BwdHY0vv/xSME5LbVi/fj0sLCx49zygJq2/+IYg1vAyMzMxZMgQtGnTBjt27HiveCgb61CqkFUnDwgI4LQ6eUZGBnx8fHDhwgWMGDECe/fuRbNmzTiLB9DOTi5kHjx4AJFIhDt37mDSpEkIDg5Wm+BldnImq8wIUU1T/1u3W7dunUYlo2RqTiwWy9VcbGwsateubVAVRwDg7NmzyMjIYMWLoAlCUnOqEMTVcfr0aaSkpCAlJeWDJqFc3dHKqpNz0YKloqICp06dgp+fH2rWrIk5c+bA1dW10ouOzffoypUrSEhIQFBQEGvHVAVT51xSUoLo6GiEhISgRYsWsLa2Rp8+farcTyKRwMbGhvHuEEJMeN7e3ujWrRsGDRqkdjuZmouNjUWvXr3g5OSETp06AXj3/gpV3VbGy5cvsXHjxkrrZLJ5vrLWX3/88YdGrb+YRJ/zFkTCmz17NmbPns11GHK4qk6urOb27dv3Xt1Frnn9+jVcXFwQHR0tyB9eddy/fx9isRh37tzB5MmTq1RzyqxatQpz5sxBhw4dGIxSeNy5cwfx8fGIjo5W+e8UReHatWsQi8XIysqCpaUl76ug0IGsafTu3btRr149zmJQbuSsS7F4utFnCUkQCY9PsF2dXKbmfH19UbNmTcydO1etmuMKiqKwYMECbN26VW87OV/QVc0pc+LECRQUFMDc3JyBKIVLYWEhHBwcEBwc/MH1nJeXh6CgIMTGxuKrr77CihUr5GrOGNi6dSvGjh2LHj16sH5s5dZffFqbe/z4MUJCQnTenyQ8LSgtLcXChQvh7e3N+FpBRkYGvL29cfHiRYwcORL79+/XWc2xobb279+Pr7/+Gv369WP8WJqgzznL1Nzdu3c1WptTR0ZGBjw8PBjvDiFDSNN6Dg4OcHV1la85K6q57OxsTJ8+HfHx8RpNARvSjMKlS5eQnJwMZ2dntdvRec66NnJmE1nT6B07duCrr77SaQyS8LTAyckJ9vb2jFUnr6iowMmTJ+Hn54datWph7ty5WLVqFa8uOlXoYyfnCzI1FxwcjFatWsHKykonNacI3+3kXBIYGIiWLVti6NChH6g5Z2dnmJqach0iJ+Tk5GDNmjWsdYfQt5Ezmzg7O2PBggV6Pc5DEp6GyKqTjxs3jvax09PT4ePjQ4uaYxtd7eR84f79+xCJRLh37x4mT56MkJAQ2h6l4MJOLgSF9+DBA4SFhcHFxQVz587Fq1evYGlpqbGaM1So/zWN3rFjB6NdMuhq5MwmR44cQUVFBSZOnIjc3FydxyEJTwOYsJMLVc0poq2dnC+UlJQgKioKISEhaNWqFaytrdG7d29aj8GVnZzvNx0vX77EhAkT8Omnn+LIkSNYuXKl0ao5ZXbt2oXBgwfTfi3KkLX+oqORM5ukpaVh3759tPz+koRXBXTbyZXV3IEDB/DJJ5/QECn7aGon5wvJyckQi8VyNRcaGor69evTfpyq7OTGBkVRuHr1KsRiMc6ePQsLCwusXbvWqNWcMteuXcPVq1f1MmSogolGzmwikUgwf/58HDhwgBZnLkl4VUCHnVxRzdWuXRtz587F6tWreX83ro6q7OR8QVHNtW7dGlZWVozdQQPc28n5NKX55s0bBAUFIS4uDr1790avXr3QtGlTbN68mevQeMWbN2/g7OyMqKgo2n4TmGzkzCZr1qzBrFmzaJsFIAlPDfraydPT0+Ht7Y0///wTo0aNErSaU0SdnZwvJCcnw8vLCw8ePMCUKVMYU3PKcGknB7if0lRUc4prc+np6bC1tSWqVwmKorBw4UJs2rQJjRs31mssNho5s8mpU6fw+vXrKustawNJeJWgq528oqICJ06cgJ+fH+rUqYO5c+dizZo1nP8Q0YmynZwvlJSUIDIyEqGhoWjZsiXmzp2L/v37s3Z8Te3khsibN29w+PBhHDlyBH369IGLiws6duwI4D87uUgkQs2aNTmOlF8cOnQIvXv3xjfffKPzGMrF4vfs2cO776a2ZGZmYtu2bYiPj6d1XJLwVKCLnfzZs2fw8fGRq7mDBw/yRs3ROc2laCfnC/fu3YNYLEZycrJczbFdiYNtO3llsHlsiqJw5coViMVi5OTkYMaMGSqdljI7edu2bRmNRWgkJibi999/R0REhNb7ym6sZY2cFYvFC52KigpYW1tj3759qFu37gf/bvClxdhGUzu5spqbN2+ewak5RWR28ri4OK5DQXFxsXxtrk2bNrC2tn7vYVRZZ3U2YMtOzheU1Zyrq6tczSmjaCcn/Mfbt2+xdOlShIWFaZWkFNXc0KFDsWvXrg/qCwudDRs2wNzcHN26daN9bJLwlNDETv7s2TN4e3vj0qVLGD16NK/UnCroSMDFxcWws7ODn58fp90h7t27B5FIhPv378Pc3BxhYWEq1+bYvOnYuXMno3ZybWBK6SiqudzcXI2em6PTTl4VQrrJlD3O4+bmplF7NOXWX3PmzIGLiwukUikL0bLLuXPn8PTpU7i5uVW6jT6fNUl4Cqizk5eXl8unEOrWrYu5c+fCzc1NUF80fVi2bBmWLFmCli1bsn7s4uJi+dpc27ZtYWVlpXNpIbq5du0arl27RrudnC/I1FxcXBz69u2rVs0pInuchy47uSHh6+uLTp064fvvv1e7nfLanHLrL0NLeFlZWVi/fj2jxiaS8P5HZXZyZTV36NAhjZvWGgoRERGoX78+Ro8ezepxZWpO5rSsTM1xBRN2cn2hQ+EpqrnXr1/D0tISx44d0+q5OTc3N8ycOZM8VK7E3bt3ERsbi5iYGJX/rq6RsyEj+/3dtWsXo99xkvD+h6Kd3NjVnCKPHz+Gj48Pa3ZyZTVnbW3Ny0aysu4QdNjJ6USfa/T169fytbl+/fph1apVOj1/eurUKeTm5tJqJzcEioqKsGjRIgQFBX2wLMDHRs5ssn37dowaNQo9e/Zk9Dgk4eE/O/n06dPh7u5u1GpOETbt5Hfv3oVYLOatmlPm4MGD6NOnj152cj5AURT+/vtvuZqbMWMGjh8/rvPn/fz5c2zfvp217hBCwtHREStXrpQ/AK5tI2dD5fLly7h9+zYCAwMZP5bRJ7yXL19i4cKFaN++PVatWmXUak4Zpu3kQlFzyiQmJuKPP/7QyU7ONJpOaSqrudWrV+vdnFZmJ9+7d69KO7kxExQUhE8//RTDhw/nfSNnNsnNzcWqVasQExPDym+u0Sa8tLQ0eHl5wdPTE9OnT4eLi4tRqzllmLST3717FyKRCP/++y/Mzc0RHh7OWVdnbXn79i2WLFmC8PBwXt6Jq/vRUFRzb9680VvNKbNx40ZMmTKFETu5kPn3338RFBSEBQsWwNzcnNeNnNlE9jjPtm3bYGJiwsoxjTLhWVpaolGjRmjYsCFWrVoFe3t7rkPiFUzYyYuLixEREYGwsDC0a9cOVlZWglBzisjs5O7u7oK6OXr9+jUCAwNx9OhR9O/fH2vWrEH79u1pPcb58+fx9OlTrFmzhtZxhc6jR48wevRoNG/eHPfv3xdU6y+m2bNnD7799lv07duXtWMaZcLbvXs3srOz4eHhgb1793IdDuNo49yj207OlZpj4nk0Te3kXCJTeBRF4a+//oKXlxcjak6R7OxsbNiwAbGxsbSPrSl8qrSiWCw+KSmJsZqWfDpnbblx4wb++usvhIWFab0vqbSiJTVq1OCdnZwv0GEnl6m50NBQtG/fHtbW1vjyyy9pjJJ9qrKT8wWpVAqJRILx48djwIABjKg55ePNnz8fHh4evDYZsYFy66/Ro0ejbdu2cHV15To0XpGXlwcnJydERkay/vtrlAlv6dKlvLOT8wF97eR37tyBSCTCw4cPMXXqVERERAhmbU4d6uzkfICiKFy+fBkHDx5EcXExatasiejoaDRq1IjxY+/YsYMVOzlfqayRc2pqKmxsbIhbVQlZd4iNGzeiSZMmrB/fKBPel19+KXg7uTZochelq528uLgY4eHhCAsLQ4cOHWBlZcULNUfnnaOynZwvvH79GgEBATh69Ci+/vprrFy5Ul5dno2uBDI7eUBAAOPHqgq2lYK6Rs5lZWWwsbHBoUOHGG1yK8TZKZFIhC+//BIDBgzQeYyHDx/qvK9RJjw7OzuuQ+AVutjJZWouJSUF5ubmBqPmlFG0k/MBxbW5/Px8zJgxAydOnEDNmjVRWFjI2rpObm4uVq9ezZqdnA9o2sjZxcUF1tbWjE4lC5GkpCScOnUKkZGRWu+r2MhZH8OYUSY8Y7YCq0JTO3lRUZHcacknNccU//77L4KDg3nRHSI3NxeBgYGIj4/H119/DTc3N5U/qGwkH1mVmW3bthlFdwhtGjnHx8ejtLQUkydPZjlKflNQUIDFixcjNDRUq9/f5ORkiMVi3Lt3T976q6ysDP7+/jrFYZQJj/AfmtjJjUXNKVJSUgJbW1t5TUMuUKXmmHJaaoPMTt6nTx9O42ASXRo5p6enY/fu3WTdTgWLFi3CmjVrNOoqo6jmWrduDSsrq/c6keTm5uocB0l4Rkx2djbWr1+vUsEoqrmOHTvCysrKqIwJy5cvh6OjIye9xpTVnLu7O9q1a6fRvkxPad64cQOXL19GaGgoo8fhCl0bOZeXl8Pa2hr79+/XuGm0seDv74927dph8ODBardLTk6GSCR6r5Ez3c5fkvCMFJmdfOfOne9dVLdv34ZIJMKjR48wdepUREZG4qOPPuIwUvaJiopC7dq1MWbMGNaOSVEULl26BC8vL7x9+xYzZ87USc0xOaXJpZ2cSXRRc8q4u7vD0tISnTt3ZjBS4ZGcnIyoqKhKH+cpKSmRlxdUpebohiQ8I2XHjh0YOXIkevbsiaKiIoSHhyM8PNwo1ZwiT548gUgkYm1aKjc3FwEBAYiPj8eAAQOwdu1ajdUcm3BtJ2cCRTWnTyPnM2fOICsrCxs2bGAgSuFSXFwMe3t7BAYGfvA4z7179yAWixlVc6ogCc8IuXz5MpKSkuDk5AR7e3ujVnOKsGUnV6XmZE5LvkKHnZwPKLb+qlOnDubNm6e1mlPkxYsX2LJlC1m3U8HixYvh5OSE5s2bA3iXAGVrc1w1ciYJzwhQXNdJT0/H3Llz0bJlS4jFYlhbW+OLL77gMDpm0GUti2k7ORtqjompRn3s5GxR1eet3MhZVzWniOxxnj179nByo8jn0mKhoaFo0qQJRowYIW/kfP/+fZibm+vd+ouUFiNUye3bt+Ht7Y3o6GhYW1tjxYoVRq3mlGHKTq6s5mbNmoWTJ09y5vzUFl3t5HyA6UbOmzdvxsSJE9G9e3daxjMUUlJS4Ovri2nTpmHMmDGcqTlVCONbR9CJoqIihIWFISwsDKampqhfvz6cnZ3h4ODAdWi8ggk7eU5ODgICAnDs2DEMGDAA69atY6yvIJNoYyfnC8pqjolGzhcvXkRKSgqpk6lEYmIiJkyYgPbt26OiooJ3jZxJwjNAkpKSIBKJ8OTJE0ydOhXh4eG4d+8ePDw8sGXLFq7DYwVN7+LptJNTFIU///wTXl5eKCwsxMyZM1lXc1KplLaxNLWT8wFZFZTAwEB89NFHmDdvHmONnLOzs7F27VrExsZy6lbli1NWsZHzs2fPsHjxYjg6OjJ2PH3OmyQ8A6GwsFDutOzUqRPmz58vX5vLycnBypUrSXcIFdBhJ1dUcwMHDsT69es5U3N0fb5V2cn5wrNnz+Dl5YVLly5h1KhR8PT0ZLRXoVQqhY2NDX777Tc0aNCAseMIgbt370IsFuPBgweYMmUKLC0tcf36dUaTnb6QhCdwZGru8ePH+PnnnxEVFfXe2pysaenatWsNxk5OF/rYyfmg5phCnZ2cD5SXl+P48ePw9/dHvXr15B0KqlWrxvj77+HhgeHDhwuueTFdKKq5tm3bwtraGr169UJqaiqsra1571YV/rfTCFFWczY2NujRo4fKbUUiEXr27ImBAweyHCW/0dVOLlNzx48f51zNqYIO556ynZwvpKWlwdvbG3/99Rd+/PHH99RceXk548e/cuUKEhISEBQUxPix+Ia6Rs6yptEHDx5k9HEeOiAJT0DcunULIpEIT58+VanmlElKSsLJkyd16ipsyGhrJ6coChcvXoSXlxeKioowa9YsnDhxgpdqTt8pTUU7OR9Qpebc3d1Zn5p//fo1XFxcEB0dbTTLArJGzmFhYWjXrh2srKxUKttVq1Zhzpw56NChA/tBagn/vrGE9ygsLERYWBgiIiLQuXNnLFiwoFI1p0hBQQEcHR0FaSdnGk3t5Dk5OfD398fx48fx7bffYuPGjWjTpg1LUbJPSkoKAgICcOTIEa5DUavm2EbWHWLr1q2sNNXlGnVqTpkTJ06goKAA5ubmLEepGyTh8RRt1ZwyMjv5p59+ysp0j1Coyk6uSs0JaW1O1ynN0tJSLFy4EN7e3pydq7KamzdvHidqTpn9+/fj66+/Rr9+/TiNg0lkai40NBTt27eHtbV1la2/MjIy4OHhwft1O0WE8S02EnRVc8r4+/ujbdu2GDJkCAB+V2RgClXnrM5O/urVK/nanJDVnK5qXlZmrnXr1jRHVDVpaWnw8vLC5cuXMWbMGIhEInz88cdajcHUNZ6QkIALFy4gPDyckfH1gY5zlrX+evjwIaZOnapx66/y8nLMnz8f+/btY707BKm0InCU1Vx0dLTGnceVSU5ORmRkJGJjY+kNUuCospMrqrni4mLBqTm6iI2NRY0aNTBu3DjWjlleXo5jx44hICBArubWrl3LuZpTJD8/H8uWLUNERASv4tKX4uJihIeHIywsTGM1p8z69ethYWGBLl26MBQlMxjXN5tHKKu5hQsX6l2iqLi4GHZ2dry1k3OJop381atX8Pf3x4kTJzBo0CDBqjk6SE1NxcGDB1mblkpNTYW3t7deao4NZI/zrFu3jpfx6QJdjZzPnj2LjIwMrF27loEomYUkPJa5desWPD09kZqaCgsLC73UnDIyO3mLFi3ee92Q7k41RfGcZXZyKysrzJgxQ67mHBwcDE7NaTPdw5adXKbm/P39Ub9+fUbUHN3XuLe3N7p164ZBgwbROi6daHLOio2cO3ToACsrK63VnCIvX77Exo0bOTU2kUorPKegoECu5rp27QpbW1vaC86GhoaicePGGDlyJK3jCp2UlBRYWlqiZcuWuHDhglGrOWWYtpOnpqbCy8sLf//9N8aMGQOxWCwItXTnzh3Ex8cjOjqa61B0hi41p4isafTu3bv1HosrSMJjkMTERIhEIrmai4mJoU3NKZKSkgJ/f39e2Mn5AEVRuHDhgrzklKOjo0GqOX1gyk5eXl6O+Ph4BAQEoEGDBpg3bx7WrVsnmFmGwsJCODg4IDg4WHCP8yirOWtra1obOW/duhVjx47VyUjHF8gvAM3I1FxkZCS6dOnCiJpTRGYn9/Ly4nUDUTZQXJsbOHAgunbtiv79+2Px4sVch8YamkxpMmEnV1RzY8eOFYyaU8bBwQGurq5o1qwZ16FozO3btyESieSNnOlQc8pcunQJycnJcHZ2pnVctiEJjyaU1Ryda3PqcHJygp2dndFO01EUhfPnz8Pb2xslJSWYPXs2HBwckJCQgG3btiEiIoLrEFmlKiVFp51cIpHInZZCVHPKBAYGomXLlhg6dCjXoVRJUVERQkJCEBkZCVNTU1hZWdGq5hTJycnBmjVrOO8OQQck4emB8tqcnZ0dPv/8c9aOHxsbi+rVq2P8+PGsHZMvvHr1Cn5+fjh58iS+++47bN68Wf4MWX5+PlasWIHQ0FDBf0Hphg47+dOnT+Ht7S1Xc15eXoIvTP7gwQOEhYUhLi6O61DUoqjmJk+ejLCwMDRs2JCx41EUBRsbG+zYsYPR47AFSXg6cPPmTYhEIqSlpWHatGmMrc2pIzU1FQcOHEB8fDyrx+USVWrO0dHxvbU5mZ3czc1NkFNq+qJuSlMfO7mymrOyshK0mlNE9jiPn58fLx/nKSoqkj83Z2pqCmtra3zxxResVFDatWsXBg8ejN69ezN+LDYQTMIbP348EhMTkZWVhcaNG2P48OHYunXrBxZ8pigoKEBoaCgiIyPRrVs32Nvbs6rmFJFIJJg/f74gqpPTQXZ2Nvz9/VWqOWWEYCdnksoSkK528qdPn8LLywtXr141GDWnzLJly7BkyRK0bNmS61De4/bt2/D09Ky09RfTXLt2DVevXkVISAhrx2QawSQ8MzMzuLi4oHnz5sjIyMCyZcswZcoUXL58mdHjytTcs2fPGHVaaoPMTt6xY0eNthdiaTFFNVdaWopZs2Zh8eLFau/AFe3kFRUVLEbLH1QlPG3t5BKJRO60NDExwbx587B+/Xpeqzldr/GIiAjUr18fo0ePpjki3SgqKkJYWBjCw8Nhamr6XiNnZZj8Xr958wbOzs68bBqt13lTAiUuLo6qVq0aVVZWpvE+eXl5FAAqLy9P7XZv376lxGIxNXLkSMrR0ZG6e/euvuHSxvHjx6kFCxZotU9ZWZlW7xOXZGVlUdu3b6eGDRtGubu7U2lpaRrtV1BQQA0dOpR68eIFRVHCOme6KCgooBo1akQ1atSIKigokL++adMmSiwWV7n/kydPKFdXV2r48OHUrl27qJycHCbDpRVdPu9Hjx5Ro0aN4sV1cuvWLcrW1pb68ccfKT8/P6qwsLDKfZi6xqVSKTVt2jTq77//pn1sOnj16pVGv+OqEIzCUyQ3NxdBQUEYOHCgWit+aWkpSktL5f+fl5cn318ikXxw53Lr1i0EBAQgIyMDkyZNgre3t9zJlpubW+lxKIU7jqruhnTZVrZdZmYmtmzZguDg4PfiqWpMiUQCAKhZs6bGx2frnGSvXbp0CYcPH0ZZWRksLCwQHBwsV3Pq3nvZ/g4ODrCzs0PNmjXlny+A964PNs+JrjGr2lZxu6KiItSvXx/Au/5tpaWl+Pvvv5GYmIgDBw4gJyfngzElEglOnTqFsLAwNGjQADNmzJA/xkFRlEbvPZPnpOmYsvUsdb8Hip9TWVkZ5s2bBw8PD7x9+1bv41e1rartCgsLERsbi7i4OHTo0AEzZsxA9+7dQVEUiouLUVxcrHZM2TX+f//3f7Ree97e3ujSpQs6derEi989ZV6/fv3BmBqjS4blCicnJ+qjjz6iAFDffPMN9erVK7Xbu7m5UQDIH/kjf+SP/BnY36NHj7TOIdUoirsFHnd39yodY9evX0ffvn0BvLOi5+bmIjU1FWvXroWJiQni4+MrvRNQVnhv3rxB27ZtkZaWBhMTE/pOhOfk5+ejdevWePbsmUFYizXBGM8ZIOdtTOdtjOcMvJupa9OmDV6/fq11Q15OE96rV6/w6tUrtdu0a9dO5QOy6enpaN26NS5fvowBAwZodLz8/HyYmJggLy/PqC4QYzxvYzxngJy3MZ23MZ4zoN95c7qG17RpUzRt2lSnfWV5WlHBEQgEAoFQGYIwrVy7dg3Xrl3DoEGD0LhxYzx+/Bhr1qxBx44dNVZ3BAKBQDBuBFEOvG7duoiOjsawYcPQpUsXzJkzBz169MCFCxdQu3ZtjcepXbs23NzctNrHEDDG8zbGcwbIeRvTeRvjOQP6nTena3gEAoFAILCFIBQegUAgEAj6QhIegUAgEIwCkvAIBAKBYBSQhEcgEAgEo4AkPAKBQCAYBUab8MaPH482bdqgTp06aN68OWbMmIHMzEyuw2KUp0+fYu7cuWjfvj3q1q2Ljh07ws3NDWVlZVyHxjgbN27EwIED8dFHH2ldjkgoHDhwAO3bt0edOnXQp08f/Pnnn1yHxDgXL17EuHHj0KJFC1SrVg2xsbFch8Q4mzdvRr9+/dCgQQN8+umnmDhxIh48eMB1WIxy8OBB9OzZEw0bNkTDhg0xYMAAnDhxQutxjDbhmZmZITw8HA8ePEBUVBQePXqEKVOmcB0Wo9y/fx9SqRSenp64e/cudu7ciUOHDsHFxYXr0BinrKwM5ubmWLBgAdehMEJYWBgcHR3h6uqKmzdv4rvvvsPo0aORlpbGdWiMUlhYiC+//BL79u3jOhTWuHDhAmxtbXHlyhWcOXMG5eXlGDFiBAoLC7kOjTFatWqFLVu24MaNG7hx4waGDh2KCRMm4O7du9oNpHW5aQNFl/56hsC2bduo9u3bcx0Ga/j6+lImJiZch0E7/fv3p2xsbN57rWvXrpSzszNHEbEPAComJobrMFgnKyuLAkBduHCB61BYpXHjxpSXl5dW+xitwlNE0/56hkheXh6aNGnCdRgEPSgrK8M///yDESNGvPf6iBEjcPnyZY6iIrCFrM+nsXyPKyoqEBoaisLCQq1LSxp1wluxYgXq1auHjz/+GGlpaYiLi+M6JFZ59OgR9u7dCxsbG65DIejBq1evUFFRgWbNmr33erNmzfDixQuOoiKwAUVRWLJkCQYNGoQePXpwHQ6j3L59G/Xr10ft2rVhY2ODmJgYfP7551qNYVAJz93dHdWqVVP7d+PGDfn2y5cvx82bN3H69GnUqFEDM2fO1K2LLsdoe97Au+7po0aNgrm5OebNm8dR5Pqhy3kbMsp9ISmKqrK7NEHY2NnZISkpCSEhIVyHwjhdunRBYmIirly5ggULFmDWrFm4d++eVmMIoluCptjZ2cHCwkLtNu3atZP/t6w9UefOndGtWze0bt0aV65cEVwHBm3POzMzE2ZmZhgwYABEIhHD0TGHtudtqDRt2hQ1atT4QM1lZWV9oPoIhoO9vT2OHDmCixcvolWrVlyHwzi1atWCqakpAKBv3764fv06du/eDU9PT43HMKiEZ6z99bQ574yMDJiZmaFPnz7w9fVF9erCFfn6fN6GRK1atdCnTx+cOXMGP/30k/z1M2fOYMKECRxGRmACiqJgb2+PmJgYnD9/Hu3bt+c6JE6gKErr32uDSniaYqz99TIzMzFkyBC0adMGO3bsQHZ2tvzfPvvsMw4jY560tDTk5uYiLS0NFRUVSExMBACYmpqifv363AZHA0uWLMGMGTPQt29fuXJPS0sz+PXZgoICpKSkyP//yZMnSExMRJMmTdCmTRsOI2MOW1tbBAcHIy4uDg0aNJArexMTE9StW5fj6JjBxcUFo0ePRuvWrfH27VuEhobi/PnzOHnypHYD0e4VFQBJSUmUmZkZ1aRJE6p27dpUu3btKBsbGyo9PZ3r0BjF19eXAqDyz9CZNWuWyvM+d+4c16HRxv79+6m2bdtStWrVonr37m0UNvVz586p/FxnzZrFdWiMUdl32NfXl+vQGGPOnDnya/uTTz6hhg0bRp0+fVrrcUg/PAKBQCAYBcJdwCEQCAQCQQtIwiMQCASCUUASHoFAIBCMApLwCAQCgWAUkIRHIBAIBKOAJDwCgUAgGAUk4REIBALBKCAJj0AgEAhGAUl4BAKBQDAKSMIjEARKSEgI6tSpg4yMDPlr8+bNQ8+ePeVNQQkEwn+Q0mIEgkChKAq9evXCd999h3379mHt2rXw8vLClStX0LJlS67DIxB4h1F2SyAQDIFq1aph48aNmDJlClq0aIHdu3fjzz//lCe7n376CefPn8ewYcMQGRnJcbQEAvcQhUcgCJzevXvj7t27OH36NAYPHix//dy5cygoKIC/vz9JeAQCyBoegSBoTp06hfv376OiouKD7uZmZmZo0KABR5ERCPyDJDwCQaAkJCTA3Nwcnp6eGDlyJFavXs11SAQCryFreASCAHn69CnGjBkDZ2dnzJgxA59//jn69euHf/75B3369OE6PAKBlxCFRyAIjNzcXIwePRrjx4+Hi4sLAKBPnz4YN24cXF1dOY6OQOAvROERCAKjSZMmSE5O/uD1uLg4DqIhEIQDcWkSCAbKyJEjkZCQgMLCQjRp0gQxMTHo168f12ERCJxBEh6BQCAQjAKyhkcgEAgEo4AkPAKBQCAYBSThEQgEAsEoIAmPQCAQCEYBSXgEAoFAMApIwiMQCASCUUASHoFAIBCMApLwCAQCgWAUkIRHIBAIBKOAJDwCgUAgGAUk4REIBALBKPh/rFes7xmfLYcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(X_grid @ V_T.T @ S @ U.T, \n",
    "          X_circle @ V_T.T @ S @ U.T, \n",
    "          X_vec @ V_T.T @ S @ U.T, \n",
    "          '$USV^T$')  # 绘制应用 U @ S @ V^T 后的图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
